A basketball player 6.2 ft tall has a shadow of 9 ft. Find the height of a tree if its shadow is 11.25 ft long. i ft
A basketball player 6.2 ft tall has a shadow of 9 ft. Find the height of a tree if its shadow is 11.25 ft long. i 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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![**Problem Statement:**
A basketball player 6.2 ft tall has a shadow of 9 ft. Find the height of a tree if its shadow is 11.25 ft long.
**Solution:**
To find the height of the tree, we can use the concept of similar triangles. Since the basketball player and the tree are both casting shadows due to the same light source (assuming the sun), their height-to-shadow ratios will be equal.
Let \( h \) be the height of the tree.
\[
\frac{\text{Height of the basketball player}}{\text{Shadow of the basketball player}} = \frac{\text{Height of the tree}}{\text{Shadow of the tree}}
\]
\[
\frac{6.2}{9} = \frac{h}{11.25}
\]
Now, solve for \( h \):
\[
h = \frac{6.2}{9} \times 11.25
\]
\[
h \approx 7.75 \text{ ft}
\]
Therefore, the height of the tree is approximately 7.75 feet.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbb8f64bb-a739-44c8-9c71-41ea58cbca19%2Fae5207bd-1725-41b3-a405-a714057b2240%2F2cjoc6b_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A basketball player 6.2 ft tall has a shadow of 9 ft. Find the height of a tree if its shadow is 11.25 ft long.
**Solution:**
To find the height of the tree, we can use the concept of similar triangles. Since the basketball player and the tree are both casting shadows due to the same light source (assuming the sun), their height-to-shadow ratios will be equal.
Let \( h \) be the height of the tree.
\[
\frac{\text{Height of the basketball player}}{\text{Shadow of the basketball player}} = \frac{\text{Height of the tree}}{\text{Shadow of the tree}}
\]
\[
\frac{6.2}{9} = \frac{h}{11.25}
\]
Now, solve for \( h \):
\[
h = \frac{6.2}{9} \times 11.25
\]
\[
h \approx 7.75 \text{ ft}
\]
Therefore, the height of the tree is approximately 7.75 feet.
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