**Activity Instructions: Determine the Height**### Objective:In this activity, you are asked to determine the height of a building using the given information.### Diagram Explanation:- The diagram shows a right triangle formed between a point on the ground (where measurements are taken) and the top of a building.- The horizontal distance from the measurement point to the base of the building is represented as $ s $.- The height you want to determine is marked as $ h $.- Two angles are measured from the ground to the top of the building: - $ \alpha $ (the angle of elevation from the ground to the top of the building) - $ \beta $ (an additional angle which seems to be required but is unspecified in this context)### Parameters:- **Distance $ s $:** The horizontal distance from the measurement point to the building is given as 60 feet.- **Height of the observer:** The height of the team member who measures the angle is 6 feet.- **Angles:** You will find $ \alpha $ and $ \beta $. (Note: Specific values are needed to proceed with calculations)### Tasks:1. Use the given distance and height of the observer to calculate the angle of elevation to the top of the building.2. Determine the height $ h $ of the building using trigonometric relationships.

We have, s=60 ft., α=23°, β=29° and height of team member is 6 ft. Let us consider that CD=x then, BD=s+x and AD=h-6.In right angled triangle △ADC, tanβ=ADCDtan29°=h-6xx=h-6tan29° ⋯⋯1 In right angled triangle △ABD, tanα=ADBDtan23°=h-6s+xs+x=h-6tan23°x=h-6tan23°-sx=h-6tan23°-60 ⋯⋯2 From equation (1) and (2), we get the result as h-6tan29°=h-6tan23°-60h-6tan23°-h-6tan29°=60h-6tan29°-tan23°tan29°·tan23°=60h-6=60tan29°·tan23°tan29°-tan23°h=60·tan29°·tan23°tan29°-tan23°+6 ft. On substituting the values of tan29° and tan23° from calculator, we get the value of h as h=60·tan29°·tan23°tan29°-tan23°+6 ft.h=600.5543·0.42440.5543-0.4244+6 ft.h=114.73 ft. Hence, value of h will be h=114.73 ft.

Answered: In this activity you are asked to…

Math

Trigonometry

In this activity you are asked to determine the height h • s will be given to you outside s = 60 ft • assume that the height of the team member that measured the angle = 6 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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Concept explainers

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.

Question

**Activity Instructions: Determine the Height**

### Objective:
In this activity, you are asked to determine the height of a building using the given information.

### Diagram Explanation:
- The diagram shows a right triangle formed between a point on the ground (where measurements are taken) and the top of a building.
- The horizontal distance from the measurement point to the base of the building is represented as $ s $.
- The height you want to determine is marked as $ h $.
- Two angles are measured from the ground to the top of the building:
- $ \alpha $ (the angle of elevation from the ground to the top of the building)
- $ \beta $ (an additional angle which seems to be required but is unspecified in this context)

### Parameters:
- **Distance $ s $:** The horizontal distance from the measurement point to the building is given as 60 feet.
- **Height of the observer:** The height of the team member who measures the angle is 6 feet.
- **Angles:** You will find $ \alpha $ and $ \beta $. (Note: Specific values are needed to proceed with calculations)

### Tasks:
1. Use the given distance and height of the observer to calculate the angle of elevation to the top of the building.
2. Determine the height $ h $ of the building using trigonometric relationships.

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