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A person standing 164 feet from the base of a church observed the angle of elevation to the church's steeple to be 36°. How tall is the church? (Give your answer to the nearest whole number) feet

A person standing 164 feet from the base of a church observed the angle of elevation to the church's steeple to be 36°. How tall is the church? (Give your answer to the nearest whole number) feet

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter1: Trigonometry
Section1.3: Right Triangle Trigonometry
Problem 72E: A 20 meter line is used to tether a helium-filled balloon. The line makes an angle of approximately...
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### Trigonometric Problem: Calculating the Height of a Church Steeple **Problem Statement:** A person standing 164 feet from the base of a church observed the angle of elevation to the church's steeple to be 36°. How tall is the church? (Give your answer to the nearest whole number) **Solution Explanation:** To find the height of the church, we can use trigonometric functions, specifically the tangent function, which relates the angle of elevation to the height of the steeple and the distance from the observer to the base of the church. The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. Here, the opposite side is the height \( h \) of the church steeple, and the adjacent side is the distance \( d \) from the observer to the base of the church. Mathematically, this is expressed as: \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{h}{d} \] Given: - \( \theta = 36^\circ \) - \( d = 164 \) feet We need to find \( h \). Rearranging the formula to solve for \( h \): \[ h = d \cdot \tan(\theta) \] Plug in the known values: \[ h = 164 \cdot \tan(36^\circ) \] Using a calculator with the tangent function: \[ h \approx 164 \cdot 0.7265 \] \[ h \approx 119.16 \] To the nearest whole number, the height of the church steeple is: \[ h \approx 119 \] feet. **Answer:** \[ 119 \] feet **Next Steps:** - [ ] Proceed to the next question by clicking the "Next Question" button. Now students, you can work on solving similar problems by following the same steps. This understanding of trigonometric applications is useful in many real-life scenarios, such as engineering and architecture.
Transcribed Image Text:### Trigonometric Problem: Calculating the Height of a Church Steeple **Problem Statement:** A person standing 164 feet from the base of a church observed the angle of elevation to the church's steeple to be 36°. How tall is the church? (Give your answer to the nearest whole number) **Solution Explanation:** To find the height of the church, we can use trigonometric functions, specifically the tangent function, which relates the angle of elevation to the height of the steeple and the distance from the observer to the base of the church. The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. Here, the opposite side is the height \( h \) of the church steeple, and the adjacent side is the distance \( d \) from the observer to the base of the church. Mathematically, this is expressed as: \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{h}{d} \] Given: - \( \theta = 36^\circ \) - \( d = 164 \) feet We need to find \( h \). Rearranging the formula to solve for \( h \): \[ h = d \cdot \tan(\theta) \] Plug in the known values: \[ h = 164 \cdot \tan(36^\circ) \] Using a calculator with the tangent function: \[ h \approx 164 \cdot 0.7265 \] \[ h \approx 119.16 \] To the nearest whole number, the height of the church steeple is: \[ h \approx 119 \] feet. **Answer:** \[ 119 \] feet **Next Steps:** - [ ] Proceed to the next question by clicking the "Next Question" button. Now students, you can work on solving similar problems by following the same steps. This understanding of trigonometric applications is useful in many real-life scenarios, such as engineering and architecture.
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