The horizontal shadow of a vertical tree is 23.4 m long while the angle of elevation to the sun is 56.3°. How tall is the tree? Round to the nearest meter. *Student can enter max 2000 characters X DG BIU Q Use the paperclip button below to attach files.
The horizontal shadow of a vertical tree is 23.4 m long while the angle of elevation to the sun is 56.3°. How tall is the tree? Round to the nearest meter. *Student can enter max 2000 characters X DG BIU Q Use the paperclip button below to attach files.
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
![### Solving Trigonometry Problems: Calculating Tree Height Using Shadows
**Problem Statement:**
A vertical tree casts a horizontal shadow that is 23.4 meters long. The angle of elevation from the tip of the shadow to the top of the tree is 56.3 degrees. How tall is the tree? Round your answer to the nearest meter.
#### Solution Steps:
1. We can solve this problem using trigonometric principles, specifically the tangent function, which relates the height of the tree to the length of its shadow and the angle of elevation.
2. The formula for tangent is:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]
where:
- \(\theta\) is the angle of elevation (56.3 degrees in this case).
- The "opposite" side is the height of the tree (\(h\)).
- The "adjacent" side is the length of the shadow (23.4 meters).
3. Rearranging the formula to find the height of the tree (\(h\)):
\[
h = \tan(\theta) \times \text{adjacent}
\]
4. Substituting the given values:
\[
h = \tan(56.3^\circ) \times 23.4
\]
5. Using a calculator, we find:
\[
\tan(56.3^\circ) \approx 1.5097
\]
6. Therefore:
\[
h \approx 1.5097 \times 23.4 \approx 35.3
\]
7. Rounding to the nearest meter, the height of the tree is:
- **35 meters**
This problem showcases the practical application of trigonometric functions to solve real-world problems involving angles and distances.
*(Note: The above solution assumes the availability of a scientific calculator or trigonometric tables to find the tangent of the given angle.)*
#### Submission Instructions:
Students can enter up to 2000 characters in their response and are encouraged to attach relevant files if needed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffd95c06f-a3ea-4120-9338-f910c4caee1b%2F4e2a3bd1-e16c-49b1-8a71-4e2efaf1c646%2Fitkyfsr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solving Trigonometry Problems: Calculating Tree Height Using Shadows
**Problem Statement:**
A vertical tree casts a horizontal shadow that is 23.4 meters long. The angle of elevation from the tip of the shadow to the top of the tree is 56.3 degrees. How tall is the tree? Round your answer to the nearest meter.
#### Solution Steps:
1. We can solve this problem using trigonometric principles, specifically the tangent function, which relates the height of the tree to the length of its shadow and the angle of elevation.
2. The formula for tangent is:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]
where:
- \(\theta\) is the angle of elevation (56.3 degrees in this case).
- The "opposite" side is the height of the tree (\(h\)).
- The "adjacent" side is the length of the shadow (23.4 meters).
3. Rearranging the formula to find the height of the tree (\(h\)):
\[
h = \tan(\theta) \times \text{adjacent}
\]
4. Substituting the given values:
\[
h = \tan(56.3^\circ) \times 23.4
\]
5. Using a calculator, we find:
\[
\tan(56.3^\circ) \approx 1.5097
\]
6. Therefore:
\[
h \approx 1.5097 \times 23.4 \approx 35.3
\]
7. Rounding to the nearest meter, the height of the tree is:
- **35 meters**
This problem showcases the practical application of trigonometric functions to solve real-world problems involving angles and distances.
*(Note: The above solution assumes the availability of a scientific calculator or trigonometric tables to find the tangent of the given angle.)*
#### Submission Instructions:
Students can enter up to 2000 characters in their response and are encouraged to attach relevant files if needed.
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