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Question 1 of 9
1. Question
Solve for `d`Round your answer to two decimal places `d =` (12.86)
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Sin Ratio
$$sin=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$Cos Ratio
$$cos=\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$Tan Ratio
$$tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$First we need to identify which trig ratio to use.One of the known angles `(37°42′)` has `d` as an `\text(adjacent)` side and the other length `(15.5)` is the `\text(hypotenuse)`Hence, we can use the `cos \text(ratio)` to solve for `d``cos theta` `=` $$\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$ `cos \text(ratio)` `cos (37°42′)` `=` $$\frac{\color{#00880a}{d}}{\color{#e85e00}{15.5}}$$ Plug in the values Get `d` by itself to find its value`cos (37°42′)` `=` `d/15.5` `15.5 xx cos (65°)` `=` `d` Multiply both sides by `15.5` `15.5 xx 0.829` `=` `d` Evaluate `cos(37°42′)` on the calculator `12.86` `=` `d` Round to two decimal places `d` `=` `12.86` `d=12.86` 
Question 2 of 9
2. Question
Solve for `theta`Round your answer to the nearest degree `theta=` (24)`°`
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Sin Ratio
$$sin=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$Cos Ratio
$$cos=\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$Tan Ratio
$$tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$First we need to identify which trig ratio to use.One of the known lengths `(22)` is `\text(opposite)` to `theta` and the other length `(55)` is the `\text(hypotenuse)`Hence, we can use the `sin \text(ratio)` to solve for `theta``sin theta` `=` $$\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$ `sin \text(ratio)` `sin theta` `=` $$\frac{\color{#004ec4}{22}}{\color{#e85e00}{55}}$$ Plug in the values `sin theta` `=` `0.4` Use the inverse function for `sin` on your calculator to get `theta` by itself`theta` `=` `sin^(1) (0.4)` The inverse of `sin` is `sin^(1)` `theta` `=` `23.578°` Use the `\text(shift) sin` function on your calculator `theta` `=` `24°` Rounded to the nearest degree `theta=24°` 
Question 3 of 9
3. Question
Solve for `a`Round your answer to two decimal places `a =` (19.37)
Hint
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Sin Ratio
$$sin=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$Cos Ratio
$$cos=\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$Tan Ratio
$$tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$First we need to identify which trig ratio to use.One of the known angles `(61°15′)` has `a` as an `\text(opposite)` side and `13.5` as an `\text(adjacent)` sideHence, we can use the `tan \text(ratio)` to solve for `a``tan theta` `=` $$\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$ `tan \text(ratio)` `tan (61°15′)` `=` $$\frac{\color{#004ec4}{a}}{\color{#00880a}{13.5}}$$ Plug in the values Now we need to have `a` on one side of the equation`tan (61°15′)` `=` `a/13.5` `13.5 times tan (61°15′)` `=` `a` Multiply both sides by `13.5` `13.5 times 1.43` `=` `a` Evaluate `tan (61°15′)` on the calculator `19.37` `=` `a` Round to two decimal places `a` `=` `19.37` `a=19.37` 
Question 4 of 9
4. Question
Solve for `theta`Round your answer to the nearest minuteHint
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Correct!
Incorrect
Sin Ratio
$$sin=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$Cos Ratio
$$cos=\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$Tan Ratio
$$tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$First we need to identify which trig ratio to use.One of the known lengths `(14)` is `\text(adjacent)` to `theta` and the other length `(16.5)` is `\text(opposite)` to `theta`Hence, we can use the `tan \text(ratio)` to solve for `theta``tan theta` `=` $$\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$ `tan \text(ratio)` `tan theta` `=` $$\frac{\color{#004ec4}{16.5}}{\color{#00880a}{14}}$$ Plug in the values `tan theta` `=` `1.1786` Use the inverse function for `tan` on your calculator to get `theta` by itself`theta` `=` `tan^(1) (1.1786)` The inverse of `tan` is `tan^(1)` `theta` `=` `49.686` Use the `\text(shift) tan` function on your calculator `theta` `=` `49°41’9”` Use the `\text(degrees)` function on your calculator `theta` `=` `49°41’` Rounded to the nearest minute `theta=49°41’` 
Question 5 of 9
5. Question
Find the length of `x`Round your answer to one decimal place `x=` (69.3) m
Hint
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The Angles of Elevation and Depression are the angles created by the upward or downward slope of the hypotenuse.First, we need to label the components of the triangle.To solve for `x`, we need to subtract the value of `b` from the value of `a`Next, we need to identify which trig ratio to use.The `28°` angle has `a` as an `\text(adjacent)` side, the `54°` angle has `b` as an `\text(adjacent)` side, and both angles have `60 m` as their `\text(opposite)` side.Hence, we can use the `tan \text(ratio)` to solve for both `a` and `b`Solve for the value of `a` first:`tan theta` `=` $$\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$ `tan \text(ratio)` `tan28°` `=` $$\frac{\color{#004ec4}{60}}{\color{#cc0000}{a}}$$ Plug in the values `a``xx tan28°` `=` `60` Cross multiply `a` `=` `60/(tan28°)` Divide `tan28°` from both sides to isolate `a` `a` `=` `112.8 m` Rounded to one decimal place Next, use the `tan \text(ratio)` to solve for `b``tan theta` `=` $$\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$ `tan \text(ratio)` `tan54°` `=` $$\frac{\color{#004ec4}{60}}{\color{#9e8600}{b}}$$ Plug in the values `b``xx tan54°` `=` `60` Cross multiply `b` `=` `60/(tan54°)` Divide `tan54°` from both sides to isolate `b` `b` `=` `43.6 m` Rounded to one decimal place Finally, subtract the value of `b` from the value of `a` to find `x``x` `=` `a````b` `x` `=` `112.8````43.6` Plug in the values `x` `=` `69.3 m` `x=69.3 m` 
Question 6 of 9
6. Question
Solve for `x`Round your answer to one decimal place `x =` (11.7)
Correct
Correct!
Incorrect
Sin Ratio
$$sin=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$Cos Ratio
$$cos=\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$Tan Ratio
$$tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$First we need to identify which trig ratio to use.One of the known angles `(43°)` has `x` as an `\text(adjacent)` side and the other length `(16)` is the `\text(hypotenuse)`Hence, we can use the `cos \text(ratio)` to solve for `x``cos theta` `=` $$\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$ `cos \text(ratio)` `cos (43°)` `=` $$\frac{\color{#00880a}{x}}{\color{#e85e00}{16}}$$ Plug in the values Get `x` by itself to find its value`cos (43°)` `=` `x/16` `16 xx cos (43°)` `=` `x` Multiply both sides by `16` `16 xx 0.7313537016` `=` `x` Evaluate `cos(43°)` on the calculator `11.7` `=` `x` Round to one decimal place `x` `=` `11.7` `x=11.7` 
Question 7 of 9
7. Question
Solve for `h`Round your answer to the nearest metre `h=` (315, 316) m
Hint
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Incorrect
Sin Ratio
$$sin=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$Cos Ratio
$$cos=\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$Tan Ratio
$$tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$First we need to identify which trig ratio to use.One of the known angles `(32°15′)` has `h` as an `\text(opposite)` side and `500` as an `\text(adjacent)` sideHence, we can use the `tan \text(ratio)` to solve for `x``tan theta` `=` $$\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$ `tan \text(ratio)` `tan (32°15′)` `=` $$\frac{\color{#004ec4}{h}}{\color{#00880a}{500}}$$ Plug in the values Now we need to have `x` on one side of the equation`tan (32°15′)` `=` `h/500` `500 times tan (32°15′)` `=` `h` Multiply both sides by `500` `500 times 0.631` `=` `h` Evaluate `cos(43°)` on the calculator `315` `=` `h` Rounded to the nearest metre `h` `=` `315 m` `h=315 m` 
Question 8 of 9
8. Question
Solve for `theta`Round your answer to the nearest minute `theta=` (69)`°` (20)`'`
Hint
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Excellent!
Incorrect
Sin Ratio
$$sin=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$Cos Ratio
$$cos=\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$Tan Ratio
$$tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$First we need to identify which trig ratio to use.One of the known lengths `(6)` is `\text(adjacent)` to `theta` and the other length `(17)` is the `\text(hypotenuse)`Hence, we can use the `cos \text(ratio)` to solve for `theta``cos theta` `=` $$\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$ `cos \text(ratio)` `cos theta` `=` $$\frac{\color{#00880a}{6}}{\color{#e85e00}{17}}$$ Plug in the values `cos theta` `=` `0.353` Evaluate `6/17` to 3 decimal places Use the inverse function for `cos` on your calculator to get `theta` by itself`theta` `=` `cos^(1) (0.353)` The inverse of `cos` is `cos^(1)` `theta` `=` `69.3327` Use the `\text(shift) cos` function on your calculator `theta` `=` `69°19’57”` Use the `\text(degrees)` function on your calculator `theta` `=` `69°20’` Round up the minutes `theta=69°20’` 
Question 9 of 9
9. Question
Solve for angle `theta`Round your answer to the nearest minuteHint
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The Angles of Elevation and Depression are the angles created by the upward or downward slope of the hypotenuse.First, we need to label the components of the triangle.To solve for `theta`, we need to subtract the added value of `gamma` and `beta` from the total interior angle of a triangle, which is `180°`In order to find `gamma`, we need to first solve for `alpha`.Angle `alpha` has `8.5 m` as an `\text(opposite)` side and `10.2 m` as an `\text(adjacent)` side.Hence, we can use the `tan \text(ratio)` to solve for `alpha``tan``alpha` `=` $$\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$ `tan \text(ratio)` `tan``alpha` `=` $$\frac{\color{#004ec4}{8.5}}{\color{#00880a}{10.2}}$$ Plug in the values `tan``alpha` `=` `0.833` Evaluate Use the inverse function for `tan` on your calculator to get `alpha` by itself`alpha` `=` `tan^(1) (0.833)` The inverse of `tan` is `tan^(1)` `alpha` `=` `39.794` Use the `\text(shift) tan` function on your calculator `alpha` `=` `39° 48′ 20.06″` Use the `\text(degrees)` function on your calculator `alpha` `=` `39° 48’` Rounded to the nearest minute Recall that a straight line has an angle of `180°`Since we have the value of `alpha`, we can subtract that to `180°` to find the value of `gamma``gamma` `=` `180°``alpha` `gamma` `=` `180°``39°48’` Plug in the values `gamma` `=` `140° 12’` Next, identify which trig ratio to use for finding `beta`.Angle `beta` has `8.5 m` as an `\text(opposite)` side and `17.2 m` (`10.2+7`) as an `\text(adjacent)` side.Thus, use the `tan \text(ratio)` to solve for `beta``tan``beta` `=` $$\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$ `tan \text(ratio)` `tan``beta` `=` $$\frac{\color{#004ec4}{8.5}}{\color{#00880a}{17.2}}$$ Plug in the values `tan``beta` `=` `0.494` Evaluate Use the inverse function for `tan` on your calculator to get `beta` by itself`beta` `=` `tan^(1) (0.494)` The inverse of `tan` is `tan^(1)` `beta` `=` `26.298` Use the `\text(shift) tan` function on your calculator `beta` `=` `26° 17′ 53″` Use the `\text(degrees)` function on your calculator `beta` `=` `26° 18’` Rounded to the nearest minute Finally, we can subtract the added value of `gamma` and `beta` from `180°` to find the value of `theta``theta` `=` `180°(``gamma``+``beta``)` `theta` `=` `180°(``140°12’``+``26°18’``)` Plug in the values `theta` `=` `13° 30’` `theta=13° 30’`
Quizzes
 Intro to Trigonometric Ratios (SOH CAH TOA) 1
 Intro to Trigonometric Ratios (SOH CAH TOA) 2
 Round Angles (Degrees, Minutes, Seconds)
 Evaluate Trig Expressions using a Calculator 1
 Evaluate Trig Expressions using a Calculator 2
 Trig Ratios: Solving for a Side 1
 Trig Ratios: Solving for a Side 2
 Trig Ratios: Solving for an Angle
 Angles of Elevation and Depression
 Trig Ratios Word Problems: Solving for a Side
 Trig Ratios Word Problems: Solving for an Angle
 Area of NonRight Angled Triangles 1
 Area of NonRight Angled Triangles 2
 Law of Sines: Solving for a Side
 Law of Sines: Solving for an Angle
 Law of Cosines: Solving for a Side
 Law of Cosines: Solving for an Angle
 Trigonometry Word Problems 1
 Trigonometry Word Problems 2
 Trigonometry Mixed Review: Part 1 (1)
 Trigonometry Mixed Review: Part 1 (2)
 Trigonometry Mixed Review: Part 1 (3)
 Trigonometry Mixed Review: Part 1 (4)
 Trigonometry Mixed Review: Part 2 (1)
 Trigonometry Mixed Review: Part 2 (2)
 Trigonometry Mixed Review: Part 2 (3)