15) The angle of elevation from ground level to the top of a building is 62°. If the observer is standing 300 feet from the building, how tall is the building?
15) The angle of elevation from ground level to the top of a building is 62°. If the observer is standing 300 feet from the building, how tall is the building?
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°.
Related questions
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:**
The angle of elevation from ground level to the top of a building is 62°. If the observer is standing 300 feet from the building, how tall is the building?
**Explanation:**
This is a trigonometry problem involving the tangent function. The angle of elevation is the angle between the horizontal ground and the line of sight to the top of the building. To find the height of the building, use the tangent of the angle of elevation.
**Mathematical Solution:**
Given:
- Angle of elevation, θ = 62°
- Distance from the building, d = 300 feet
To find the height, h, use the formula:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]
Substitute the values:
\[
\tan(62°) = \frac{h}{300}
\]
Rearrange to solve for h:
\[
h = 300 \times \tan(62°)
\]
Calculate the height using a calculator to find the tangent of 62°.
This approach will yield the height of the building in feet.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F35e0e75f-e8c2-4dab-b2c9-b1b559720d41%2F774d252b-57bd-4b75-baeb-45e76ae78bdd%2F7boseik_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
The angle of elevation from ground level to the top of a building is 62°. If the observer is standing 300 feet from the building, how tall is the building?
**Explanation:**
This is a trigonometry problem involving the tangent function. The angle of elevation is the angle between the horizontal ground and the line of sight to the top of the building. To find the height of the building, use the tangent of the angle of elevation.
**Mathematical Solution:**
Given:
- Angle of elevation, θ = 62°
- Distance from the building, d = 300 feet
To find the height, h, use the formula:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]
Substitute the values:
\[
\tan(62°) = \frac{h}{300}
\]
Rearrange to solve for h:
\[
h = 300 \times \tan(62°)
\]
Calculate the height using a calculator to find the tangent of 62°.
This approach will yield the height of the building in feet.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, trigonometry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning