Question

A 20 ft. ladder is used against a 15 ft. wall. What is the measure of the angle made by the ladder and the ground (nearest whole degree)? How far is the ladder from the wall on the ground (to the nearest tenth)?

Answer 1

Explanation:

Given that,

The length of a ladder, H = 20 feet

The height of the wall, h = 15 ft

We know that,

`\sin\theta=(h)/(H)`

h is perpendicular and H is hypotenuse

So,

`\sin\theta=(15)/(20)\\\\\theta=\sin^(-1)((15)/(20))\\\\\theta=48.59^(\circ)`

Now using Pythagoras theoerm,

`b=√(H^2-h^2)\\\\b=√(20^2-15^2)\\\\b=13.2\ ft`

Hence, the angle made by the ladder and the ground is 48.59° and the ladder is 13.2 feet from the wall on the ground.