Note that the arn 51.9 However, from a spot 350 ft back from the ba elevation to the top of the pyramid measures 36. 4 to the nearest foot, find the height of the pyramid
Note that the arn 51.9 However, from a spot 350 ft back from the ba elevation to the top of the pyramid measures 36. 4 to the nearest foot, find the height of the pyramid
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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Concept explainers
Cylinders
A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.
Cones
A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.
Question
![### Pyramid Height Calculation
#### Problem Description:
You are given two angles of elevation and a distance measurement related to a pyramid. The task is to find the height of the pyramid using these given parameters.
1. **Angle of Elevation from the Base:** The angle of elevation from the base of the pyramid to the top measures **51.9°**.
2. **Distance Measurement:**
- From a spot 350 feet back from the base of the pyramid, the angle of elevation to the top measures **36.4°**.
#### Task:
- **Objective:** Find the height of the pyramid.
- **Instructions:** Use the given angles and distance to perform the calculations and round the result to the nearest foot.
#### Diagram Description:
- The diagram depicts a pyramid with relevant measurements and angles marked.
- The base and height of the pyramid form a right triangle with the ground level.
- The angle of elevation is measured from the ground level to the top of the pyramid.
- The second angle of elevation is measured from a point 350 feet away from the base.
### Step-by-Step Instructions:
1. **Identify Known Values:**
- \( \theta_1 = 51.9° \) (angle from the base).
- \( \theta_2 = 36.4° \) (angle from 350 feet away).
- \( d = 350 \) feet (distance away from the base).
2. **Trigonometric Calculations:**
- Use trigonometric relationships to find the height of the pyramid.
3. **Solution:**
- Calculate the height (h) using the proper trigonometric formula and the given angles.
- Approximate the height to the nearest foot.
4. **Submission:**
- Enter the calculated value in the provided blank field.
#### Answer Box:
- Please input your answer here: **[Input Field]**
Ensure you double-check your calculations for accuracy. This exercise will help you understand the application of trigonometric principles in real-world scenarios.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd24861ef-92b0-4cd8-8c54-2ac2200498ec%2F863bd435-3897-443c-8269-cc6807fd15d8%2Fgp3y7ti_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Pyramid Height Calculation
#### Problem Description:
You are given two angles of elevation and a distance measurement related to a pyramid. The task is to find the height of the pyramid using these given parameters.
1. **Angle of Elevation from the Base:** The angle of elevation from the base of the pyramid to the top measures **51.9°**.
2. **Distance Measurement:**
- From a spot 350 feet back from the base of the pyramid, the angle of elevation to the top measures **36.4°**.
#### Task:
- **Objective:** Find the height of the pyramid.
- **Instructions:** Use the given angles and distance to perform the calculations and round the result to the nearest foot.
#### Diagram Description:
- The diagram depicts a pyramid with relevant measurements and angles marked.
- The base and height of the pyramid form a right triangle with the ground level.
- The angle of elevation is measured from the ground level to the top of the pyramid.
- The second angle of elevation is measured from a point 350 feet away from the base.
### Step-by-Step Instructions:
1. **Identify Known Values:**
- \( \theta_1 = 51.9° \) (angle from the base).
- \( \theta_2 = 36.4° \) (angle from 350 feet away).
- \( d = 350 \) feet (distance away from the base).
2. **Trigonometric Calculations:**
- Use trigonometric relationships to find the height of the pyramid.
3. **Solution:**
- Calculate the height (h) using the proper trigonometric formula and the given angles.
- Approximate the height to the nearest foot.
4. **Submission:**
- Enter the calculated value in the provided blank field.
#### Answer Box:
- Please input your answer here: **[Input Field]**
Ensure you double-check your calculations for accuracy. This exercise will help you understand the application of trigonometric principles in real-world scenarios.
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