The angle relative to the horizontal from the top of a tree to a point 10 feet from its base (on flat ground) is 30°. Find the height of the tree. The height of the tree is approximately feet. (Round to one decimal place as needed.) ww.
The angle relative to the horizontal from the top of a tree to a point 10 feet from its base (on flat ground) is 30°. Find the height of the tree. The height of the tree is approximately feet. (Round to one decimal place as needed.) ww.
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
Question
![**Problem:**
The angle relative to the horizontal from the top of a tree to a point 10 feet from its base (on flat ground) is 30°. Find the height of the tree.
---
**Solution:**
Given:
- Angle with the horizontal = 30°
- Distance from the base = 10 feet
To find: Height of the tree
**Method:**
Use trigonometry (specifically the tangent function). The tangent of an angle in a right triangle is the ratio of the opposite side (height of the tree) to the adjacent side (distance from the base).
\[
\tan(30°) = \frac{\text{Height of the tree}}{10}
\]
Rearrange to solve for the height:
\[
\text{Height of the tree} = 10 \times \tan(30°)
\]
Calculate:
- \(\tan(30°) = \frac{\sqrt{3}}{3} \approx 0.577\)
- \(\text{Height} \approx 10 \times 0.577 = 5.77\) feet
The height of the tree is approximately **5.8 feet**.
(Rounded to one decimal place as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbcea6d79-c0c2-49cd-aa31-c3eca199518f%2F8a9aba20-33b9-49a0-b6cb-541a0b470334%2Fwwsox1b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem:**
The angle relative to the horizontal from the top of a tree to a point 10 feet from its base (on flat ground) is 30°. Find the height of the tree.
---
**Solution:**
Given:
- Angle with the horizontal = 30°
- Distance from the base = 10 feet
To find: Height of the tree
**Method:**
Use trigonometry (specifically the tangent function). The tangent of an angle in a right triangle is the ratio of the opposite side (height of the tree) to the adjacent side (distance from the base).
\[
\tan(30°) = \frac{\text{Height of the tree}}{10}
\]
Rearrange to solve for the height:
\[
\text{Height of the tree} = 10 \times \tan(30°)
\]
Calculate:
- \(\tan(30°) = \frac{\sqrt{3}}{3} \approx 0.577\)
- \(\text{Height} \approx 10 \times 0.577 = 5.77\) feet
The height of the tree is approximately **5.8 feet**.
(Rounded to one decimal place as needed.)
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