Chapter 22: Chapter 22

Problem 429

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A ladder, which is leaning against a building, makes an angle of \(75^{\circ}\) with the ground. If the top of the ladder reaches a point which is 20 feet above the ground, find, to the nearest foot, the distance from the foot of the ladder to the base of the building.

Short Answer

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The distance from the foot of the ladder to the base of the building is approximately \(5\) feet.

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TABLE OF CONTENTS

Step 1: Identify the given values and what we want to find

We are given: - Angle between ladder and ground: \(75^{\circ}\) - Height from the ground to the top of the ladder: 20 feet We want to find the distance from the foot of the ladder to the base of the building.

Step 2: Set up the equation using tangent function

In right triangle trigonometry, the tangent function is defined as the ratio of the opposite side to the adjacent side. Therefore, we can write the equation involving the tangent function as: \[\tan(75^{\circ}) = \frac{\text{Opposite Side (height)}}{\text{Adjacent Side (distance)}}\] Where the Opposite Side (height) = 20 feet.

Step 3: Solve for the Adjacent Side (distance)

Now, we want to solve for the Adjacent Side (distance), so let's rewrite the equation as: \[\text{Adjacent Side (distance)} = \frac{\text{Opposite Side (height)}}{\tan(75^{\circ})}\] Now, plug in the given values and calculate the distance: \[\text{Adjacent Side (distance)} = \frac{20}{\tan(75^{\circ})}\] \[\text{Adjacent Side (distance)} \approx 5.213\]

Step 4: Round to the nearest foot

The distance is approximately 5.213 feet. Since we need to round it to the nearest foot, the final answer is: Distance from the foot of the ladder to the base of the building: \(5\) feet.

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Chapter 22: Chapter 22

A ladder, which is leaning against a building, makes an angle of \(75^{\circ}\) with the ground. If the top of the ladder reaches a point which is 20 feet above the ground, find, to the nearest foot, the distance from the foot of the ladder to the base of the building.

Short Answer

Step by step solution

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Step 1: Identify the given values and what we want to find

Step 2: Set up the equation using tangent function

Step 3: Solve for the Adjacent Side (distance)

Step 4: Round to the nearest foot

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Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

Chapter 8

Chapter 9

Chapter 10

Chapter 11

Chapter 12

Chapter 13

Chapter 14

Chapter 15

Chapter 16

Chapter 17

Chapter 18

Chapter 19

Chapter 20

Chapter 21

Chapter 23

Chapter 24

Chapter 25

Chapter 26

Chapter 27

Chapter 28

Chapter 29

Chapter 30

Chapter 31

Chapter 32

Chapter 33

Chapter 34

Chapter 35

Chapter 36

Chapter 37

Chapter 38

Chapter 39

Chapter 40

Chapter 41

Chapter 42

Chapter 43

Chapter 44

Chapter 48

Chapter 49

Chapter 50

Chapter 51

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