Question

A ladder is lear, ing against a building. The base of the ladder is 7 meters from the

base of the building. If the ladder is 20 meters tall, what is the angle the ladder makes
with the building?

Answer 1

The ladder makes an angle of approximately 69.46 degrees with the building, which is calculated using the inverse cosine (arccos) of the ratio 7/20.

Step-by-step explanation:

To find the angle that a ladder makes with a building, you can use trigonometric functions, specifically the cosine function from the cosine rule. If the ladder is 20 meters tall (which is the hypotenuse of the right triangle), and the distance from the base of the building to the bottom of the ladder is 7 meters (which is the adjacent side in relation with the angle we want to find), you can calculate the angle using the following steps:

1. 
   
3. Write down the cosine rule, which is cos(θ) = adjacent/hypotenuse.
4. 
   
6. Plug in the values: cos(θ) = 7/20.
7. 
   
9. Calculate the value of cos(θ), which is 0.35.
10. 
    
12. Use a calculator to find the angle θ by calculating the inverse cosine (arccos) of 0.35.
13. 
    
15. The angle θ is approximately 69.46 degrees.

The ladder makes an angle of approximately 69.46 degrees with the building.