As shown in the diagram below, a ladder 5 feet long leans against a wall and makes an angle of 65° with th ground. Find, to the nearest tenth of a foot, the distance from the wall to the base of the ladder. Answer 5 feet 65
As shown in the diagram below, a ladder 5 feet long leans against a wall and makes an angle of 65° with th ground. Find, to the nearest tenth of a foot, the distance from the wall to the base of the ladder. Answer 5 feet 65
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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- The ladder is represented by a diagonal line labeled "5 feet".
- There is a right angle between the wall and the ground.
- The base of the triangle (distance from the wall) makes an angle of 65° with the ladder.
To solve for the distance from the wall to the base of the ladder, we can use trigonometric functions, specifically the cosine function, since we have the hypotenuse and the adjacent side to the angle.
\[ \cos(65°) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
Let \( x \) be the distance from the wall to the base of the ladder:
\[ \cos(65°) = \frac{x}{5} \]
Rearrange to solve for \( x \):
\[ x = 5 \times \cos(65°) \]
Using a calculator:
\[ x \approx 5 \times 0.4226 = 2.113 \]
Rounding to the nearest tenth of a foot:
\[ x \approx 2.1 \text{ feet} \]
Thus, the distance from the wall to the base of the ladder is approximately 2.1 feet.
#### Answer
The distance from the wall to the base of the ladder is 2.1 feet.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F87804e42-439c-4b15-9fec-573b7a02348d%2Fa7599a70-ee99-4e2a-aec4-1efc1e30adca%2Fo2nyzck_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Ladder Against a Wall Problem
As shown in the diagram below, a ladder 5 feet long leans against a wall and makes an angle of 65° with the ground. Find, to the nearest tenth of a foot, the distance from the wall to the base of the ladder.
#### Diagram Explanation
The diagram illustrates a ladder leaning against a wall, forming a right triangle. The details provided in the diagram are:
- The ladder length (hypotenuse of the triangle) is 5 feet.
- The angle formed between the ground and the ladder is 65°.
- The height from the base of the ladder to the point where the ladder touches the wall forms a right angle with the ground.
We need to find the distance from the wall to the base of the ladder (the base of the triangle).
- The ladder is represented by a diagonal line labeled "5 feet".
- There is a right angle between the wall and the ground.
- The base of the triangle (distance from the wall) makes an angle of 65° with the ladder.
To solve for the distance from the wall to the base of the ladder, we can use trigonometric functions, specifically the cosine function, since we have the hypotenuse and the adjacent side to the angle.
\[ \cos(65°) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
Let \( x \) be the distance from the wall to the base of the ladder:
\[ \cos(65°) = \frac{x}{5} \]
Rearrange to solve for \( x \):
\[ x = 5 \times \cos(65°) \]
Using a calculator:
\[ x \approx 5 \times 0.4226 = 2.113 \]
Rounding to the nearest tenth of a foot:
\[ x \approx 2.1 \text{ feet} \]
Thus, the distance from the wall to the base of the ladder is approximately 2.1 feet.
#### Answer
The distance from the wall to the base of the ladder is 2.1 feet.
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