Trig Ratios Word Problems: Solving for an Angle

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Question 1 of 6

1. Question

A `7m` long ladder is placed against the wall. The ladder is `5m` up the wall. What is the angle, `theta`, between the ground and the ladder to the nearest minute?

`theta=` (45)`°` (35)`'`

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Help Video

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Trigonometric Ratios (SOHCAHTOA)

Sin Ratio (SOH)

$$\sin=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$

Cos Ratio (CAH)

$$\cos=\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$

Tan Ratio (TOA)

$$\tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$

Calculator Buttons to Use

`sin` `=` Sine function

`cos` `=` Cosine function

`tan` `=` Tangent function

DMS or `° ‘ ‘ ‘` `=` Degree/Minute/Second

Shift or 2nd F or INV `=` Inverse function

`=` `=` Equal function

Notice that the scenario creates a triangle. Label it in reference to the missing angle.

$$\color{#004ec4}{\text{opposite}}=\color{#004ec4}{5}$$

$$\color{#e85e00}{\text{hypotenuse}}=\color{#e85e00}{7}$$

Since we now have the opposite and hypotenuse values, we can use the `sin` ratio to find `theta`.

`sin theta`	`=`	$$\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$

`sin theta`	`=`	$$\frac{\color{#004ec4}{5}}{\color{#e85e00}{7}}$$

`sin theta`	`=`	`0.714286`
`theta`	`=`	`sin^(-1) 0.714286`	Get the inverse of `sin`

Simplify this further by evaluating `sin^(-1) 0.714286` using the calculator:

`1.` Press Shift or 2nd F (depending on your calculator)

`2.` Press `sin`

`3.` Press `0.714286`

`4.` Press `=`

The result will be: `45.5847°`

Finally, round off the answer to the nearest minute.

`theta`	`=`	`45.5847°`
	`=`	`45°35’4.9”`	Press DMS on your calculator
	`=`	`45°35’`	Round down since the seconds is less than `30”`

`45°35’`

Question 2 of 6

2. Question

A cat observes a bird’s nest on top of a tree which is `18.5 m` tall. The cat is `9.5 m` from the base of the tree. At what angle `(theta)` must the cat look up in order to see the nest? (nearest minute)

`theta=` (62)`°` (49)`'`

Hint

Help Video

Correct

Fantastic!

Incorrect