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A 22-foot ladder is resting against the side of a building. The bottom of the ladder is 3 feet from the building. Find the measure of the angle the ladder makes with the ground. Round your answer to the nearest tenth of a degree.

Verified Answer :

caylus

Hello,

We know the hypotenuse 22 ft,
the adjacent side 3 ft,
so the cosine of the angle we are going to search is 3/22
that's done cos α=3/22==>α=82.1625...°≈82.2°

The measure of the angle the ladder makes with the ground is 82.2°

What is a right angled triangle?

A triangle in which one angle is 90° is called a right angled triangle.

  • The side opposite to the right angle is the hypotenuse.

How to find the measure of the angle the ladder makes with the ground ?

According to the problem,

  • Length of the ladder is 22 feet.
  • The bottom of the ladder is 3 feet from the building.
  • A right angled triangle is formed here, in which the ladder is the hypotenuse and the base is the distance between the bottom of the ladder and the building

We know that in a right angled triangle,  

cosФ = \(\frac{base}{hypotenuse}\) , where Ф is the angle between base and hypotenuse.

Here, cosФ = \(\frac{3}{22}\)

⇒ Ф = 82.2°

∴ The measure of the angle the ladder makes with the ground is 82.2°

Find out more information about the measure of angles of right angled triangle here: https://brainly.com/question/8074395

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