A 36-ft ladder leans against a building so that the angle between the ground and the ladder is 78' How high does the ladder reach on the building? ft
A 36-ft ladder leans against a building so that the angle between the ground and the ladder is 78' How high does the ladder reach on the building? ft
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Concept explainers
Ratios
A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.
Trigonometric Ratios
Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.
Question
![**Problem Statement:**
A 36-ft ladder leans against a building so that the angle between the ground and the ladder is 78°.
**Question:**
How high does the ladder reach on the building?
[Text Box for Answer] ______ ft
**Explanation:**
This problem involves using trigonometric relationships to determine the height at which the ladder touches the building. The ladder, the ground, and the wall form a right triangle. You can use trigonometric functions, specifically the sine function, to solve for the height. The sine of an angle in a right triangle is the ratio of the opposite side (height) to the hypotenuse (ladder length):
\[
\sin(\text{angle}) = \frac{\text{opposite side}}{\text{hypotenuse}}
\]
Given:
- Hypotenuse (ladder length) = 36 ft
- Angle = 78°
Therefore, the height is calculated as:
\[
\text{Height} = 36 \, \text{ft} \times \sin(78^\circ)
\]
Using a calculator, you can find \(\sin(78^\circ)\) and then compute the height.
**Note:** Make sure your calculator is in degree mode when calculating trigonometric functions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2ed25082-0026-4235-951a-26a6d7ee0f61%2Fbd176a08-79f8-4f10-aa4d-34c2e2db6fe4%2F77z4jf75_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A 36-ft ladder leans against a building so that the angle between the ground and the ladder is 78°.
**Question:**
How high does the ladder reach on the building?
[Text Box for Answer] ______ ft
**Explanation:**
This problem involves using trigonometric relationships to determine the height at which the ladder touches the building. The ladder, the ground, and the wall form a right triangle. You can use trigonometric functions, specifically the sine function, to solve for the height. The sine of an angle in a right triangle is the ratio of the opposite side (height) to the hypotenuse (ladder length):
\[
\sin(\text{angle}) = \frac{\text{opposite side}}{\text{hypotenuse}}
\]
Given:
- Hypotenuse (ladder length) = 36 ft
- Angle = 78°
Therefore, the height is calculated as:
\[
\text{Height} = 36 \, \text{ft} \times \sin(78^\circ)
\]
Using a calculator, you can find \(\sin(78^\circ)\) and then compute the height.
**Note:** Make sure your calculator is in degree mode when calculating trigonometric functions.
Transcribed Image Text:### Right Triangle Problem
**Diagram Description:**
The image shows a right triangle labeled with sides and angles. The right angle is at the bottom left. The sides are labeled as follows:
- Side \( a \), opposite angle \( A \)
- Side \( b \), adjacent to angle \( A \)
- Hypotenuse \( c \), opposite the right angle
The angles are labeled as:
- \( A \) is at the bottom right
- \( B \) is at the top left
**Problem Details:**
- **Note:** Triangle may not be drawn to scale.
- Suppose \( c = 14 \) and \( A = 65 \) degrees.
**Find:**
- \( a = \) ___
- \( b = \) ___
- \( B = \) ___ degrees
**Instructions:**
Give all answers to at least one decimal place. Give angles in **degrees**.
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