### Find the height of the wall**Problem Statement:**At a construction site, a 30-foot ramp is leaning against a wall and makes a 32° angle with the ground.**Instructions:**Make a sketch to model this situation.Then, press "solve" to find the height of the wall.##### Input box:```height: [ ](Solve) (Submit)```**Diagram Explanation:**The diagram below demonstrates a right triangle formed by the ramp, the wall, and the ground:- The ramp is the hypotenuse of the triangle and is 30 feet long.- The angle between the ramp and the ground is 32°.- The height of the wall forms the opposite side of the angle.\[ \text{(Insert Diagram)} \]**Labels in Diagram:**- Hypotenuse (Ramp): 30 ft- Angle with ground: 32°- Opposite side, labeled as "Wall": Represents the height we need to find. The right-angled triangle approach allows us to use trigonometric functions to find the height of the wall. Specifically, the sine function will be useful here since we have the hypotenuse and want to find the opposite side.\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]\[ \sin(32°) = \frac{\text{height}}{30} \]Solve for height:\[ \text{height} = 30 \times \sin(32°) \]

Trigonometric ratios give the relation between the angles and the sides of the right angled…

Find the height of the wall. At a construction site, a 30-foot ramp is leaning against a wall and makes a 32° angle with the height: ground. Make a sketch to model this situation. Then, press "solve" to find the height of the wall. Submit Solve T

Find the height of the wall. At a construction site, a 30-foot ramp is leaning against a wall and makes a 32° angle with the height: ground. Make a sketch to model this situation. Then, press "solve" to find the height of the wall. Submit Solve T

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

### Find the height of the wall

**Problem Statement:**
At a construction site, a 30-foot ramp is leaning against a wall and makes a 32° angle with the ground.

**Instructions:**
Make a sketch to model this situation.

Then, press "solve" to find the height of the wall.

##### Input box:
```
height: [ ]
(Solve) (Submit)
```

**Diagram Explanation:**
The diagram below demonstrates a right triangle formed by the ramp, the wall, and the ground:
- The ramp is the hypotenuse of the triangle and is 30 feet long.
- The angle between the ramp and the ground is 32°.
- The height of the wall forms the opposite side of the angle.

\[ \text{(Insert Diagram)} \]
**Labels in Diagram:**
- Hypotenuse (Ramp): 30 ft
- Angle with ground: 32°
- Opposite side, labeled as "Wall": Represents the height we need to find.

The right-angled triangle approach allows us to use trigonometric functions to find the height of the wall. Specifically, the sine function will be useful here since we have the hypotenuse and want to find the opposite side.

\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]

\[ \sin(32°) = \frac{\text{height}}{30} \]

Solve for height:

\[ \text{height} = 30 \times \sin(32°) \]

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