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Trigonometry Mixed Review: Part 1 (1)Trigonometry Mixed Review: Part 1 (1)
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Question 1 of 9
1. Question
Which of the following are labelled correctly?There can be more than one answerHint
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Check each triangle and identify if the labels are correct
The side opposite of the right angle is labelled as hypThe side opposite of `theta` is labelled as oppThe side adjacent to `theta` is labelled as adjThe triangle is labelled correctly
The side opposite of the right angle is labelled as hypThe side opposite of `theta` is labelled as oppThe side adjacent to `theta` is labelled as adjThe triangle is labelled correctly
The side opposite of the right angle is labelled as hypThe side opposite of `theta` is labelled as oppThe side adjacent to `theta` is labelled as adjThe triangle is labelled correctly
The side opposite of the right angle is labelled as “opp”, but it should be hypThe side opposite of `theta` is labelled as “hyp”, but it should be oppThe side adjacent to `theta` is labelled as adjThe triangle is labelled incorrectly
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Question 2 of 9
2. Question
Solve for:`(i) \text(sin)theta``(ii) \text(cos)(90-theta)`
Enter fractions as: x/y-
`\text(sin)theta =` (3/5)
`\text(cos)(90 - theta) =` (3/5)
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
$$tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$`\text(Solving for) (i) sin theta`First we need to identify which trig ratio to use.One of the known lengths `(3)` is `\text(opposite)` to `theta` and the other length `(5)` is the `\text(hypotenuse)`
Hence, we can use the `sin \text(ratio)` to solve for `sintheta``sin theta` `=` $$\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$ `sin \text(ratio)` `cos theta` `=` $$\frac{\color{#004ec4}{3}}{\color{#e85e00}{5}}$$ Plug in the values `\text(Solving for) (ii) cos (90-theta)`First we need to understand which angle is `(90-theta)`.
Notice that the two known angles of the triangle is the right angle `(90°)` and `theta`.
Hence, the other angle left is `(90-theta)`.Now, one of the known lengths `(3)` is `\text(adjacent)` to `(90-theta)` and the other length `(5)` is the `\text(hypotenuse)`
Hence, we can use the `cos \text(ratio)` to solve for `cos(90-theta)``cos (90-theta)` `=` $$\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$ `cos \text(ratio)` `cos (90-theta)` `=` $$\frac{\color{#00880a}{3}}{\color{#e85e00}{5}}$$ Plug in the values `sintheta=3/5``cos (90-theta)=3/5` -
`\text(sin)theta =` (3/5)
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Question 3 of 9
3. Question
Solve for `x` if:`theta=30`
- `x=` (60)`°`
Hint
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The sum of the interior angles of a triangle is `180` degrees.
Identify the known values
`theta=30°``\text(right angle)=90°`To solve for `x`, we need to subtract the total value of the known angles from `180` degrees`x` `=` `180°-(``theta``+``\text(right angle)``)` `=` `180°-(``30°``+``90°``)` Plug in the values `=` `180°-120°` Evaluate `x` `=` `60°` `x=60°` -
Question 4 of 9
4. Question
Solve for `theta`
Round your answer to the nearest degree- `theta=` (37)`°`
Correct
Keep Going!
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 `(16)` is `\text(adjacent)` to `theta` and the other length `(20)` 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` `=` $$\frac{\color{#00880a}{16}}{\color{#e85e00}{20}}$$ Plug in the values `cos theta` `=` `0.8` Use the inverse function for `cos` on your calculator to get `theta` by itself`theta` `=` `cos^(-1) (0.8)` The inverse of `cos` is `cos^(-1)` `theta` `=` `36.869°` Use the `\text(shift) cos` function on your calculator `theta` `=` `37°` Rounded to the nearest degree `theta=37°` -
Question 5 of 9
5. Question
Solve for `y`
Round your answer to two decimal places- `y =` (9.41)
Hint
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Keep Going!
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 `(65°)` has `y` as an `\text(adjacent)` side and the other length `(18)` is the `\text(hypotenuse)`
[add purple angle fill for `65°`]Hence, we can use the `cos \text(ratio)` to solve for `y``cos theta` `=` $$\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$ `cos \text(ratio)` `cos (65°)` `=` $$\frac{\color{#00880a}{y}}{\color{#e85e00}{18}}$$ Plug in the values Get `y` by itself to find its value`cos (65°)` `=` `y/18` `18 xx cos (65°)` `=` `y` Multiply both sides by `18` `18 xx 0.522` `=` `y` Evaluate `cos(65°)` on the calculator `9.41` `=` `y` Round to one decimal place `y` `=` `9.41` `y=9.41` -
Question 6 of 9
6. Question
Solve for `theta`
Round your answer to the nearest degree- `theta=` (39)`°`
Correct
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 `(11)` is `\text(adjacent)` to `theta` and the other length `(9)` 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` `=` $$\frac{\color{#004ec4}{9}}{\color{#00880a}{11}}$$ Plug in the values `tan theta` `=` `0.818` Use the inverse function for `tan` on your calculator to get `theta` by itself`theta` `=` `tan^(-1) (0.818)` The inverse of `tan` is `tan^(-1)` `theta` `=` `39.2831°` Use the `\text(shift) tan` function on your calculator `theta` `=` `39°` Rounded to the nearest degree `theta=39°` -
Question 7 of 9
7. Question
Solve for `x`
Round your answer to two decimal places- `x =` (7.61)
Hint
Help VideoCorrect
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(opposite)` side and `9.5` as an `\text(adjacent)` side
Hence, 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 (43°)` `=` $$\frac{\color{#004ec4}{x}}{\color{#00880a}{9.5}}$$ Plug in the values Now we need to have `x` on one side of the equation`tan (43°)` `=` `x/9.5` `9.5 times tan (43°)` `=` `x` Multiply both sides by `9.5` `9.5 times 0.801` `=` `x` Evaluate `tan (43°)` on the calculator `7.61` `=` `x` Round to two decimal places `x` `=` `7.61` `x=7.61` -
Question 8 of 9
8. Question
Solve for `theta`
Round your answer to the nearest degree- `theta=` (55)`°`
Correct
Nice Job!
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 `(12)` is `\text(adjacent)` to `theta` and the other length `(21)` 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` `=` $$\frac{\color{#00880a}{12}}{\color{#e85e00}{21}}$$ Plug in the values `cos theta` `=` `0.5714` Use the inverse function for `cos` on your calculator to get `theta` by itself`theta` `=` `cos^(-1) (0.5714)` The inverse of `cos` is `cos^(-1)` `theta` `=` `55.152°` Use the `\text(shift) cos` function on your calculator `theta` `=` `55°` Rounded to the nearest degree `theta=55°` -
Question 9 of 9
9. Question
Solve for `b`
Round your answer to two decimal places- `b =` (119.06)
Hint
Help VideoCorrect
Fantastic!
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 `(26°25′)` has `48` as an `\text(opposite)` side and the other length `b` is the `\text(hypotenuse)`
Hence, we can use the `sin \text(ratio)` to solve for `b``sin theta` `=` $$\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$ `sin \text(ratio)` `sin (26°25′)` `=` $$\frac{\color{#004ec4}{48}}{\color{#e85e00}{b}}$$ Plug in the values Get `b` by itself to find its value`sin (26°25′)` `=` `48/b` `b xx sin (26°25′)` `=` `48` Multiply both sides by `b` `b` `=` `(48)/(sin (26°25′))` Divide both sides by `sin (26°25′)` `b` `=` `(48)/(0.403)` Evaluate `sin(26°25′)` on the calculator `b` `=` `119.06` Round to two decimal places `b=119.06`
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 Non-Right Angled Triangles 1
- Area of Non-Right 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)