A 20ft ladder is leaning against a building. If the base of the ladder is 6ft from the base of the building. What is the angle o

Question

blondinia [14]

3 years ago

9

A 20ft ladder is leaning against a building. If the base of the ladder is 6ft from the base of the building. What is the angle o

f elevation of the ladder?

Mathematics

1 answer:

deff fn [24] · Answer 1 · 2022-11-17T17:59:06+03:00

9514 1404 393

Answer:

72.5° ≈ 73°

Step-by-step explanation:

The ladder length is the hypotenuse of the right triangle that has the distance from the building as its base and the height up the building as the height of the triangle. The given dimensions are those of the side adjacent to the angle and the hypotenuse.

The appropriate trig relation is ...

Cos = Adjacent/Hypotenuse

cos(angle) = 6/20

The inverse cosine function (arccos) is used to find the angle from its cosine.

angle = arccos(6/20) ≈ 72.54°

The angle is 72.5° rounded to tenths, or 73° rounded to degrees.