Question

A 33-ft ladder leans against a building so that the angle between the ground and the ladder is 85°.how high does the ladder reach on the building ?

Answer 1

We have the next situation:

Now, we need to label the sides:

- The largest side is always the hypotenuse

- The adjacent side is between the right angle and the given angle.

- The opposite side is opposite to the given angle.

Hence,

Hypotenuse = 33 ftt

Opposite side = h

Then, we need to find h:

We need to use a trigonometric function that involves the side that we know and the missing side:

So,

sinθ = opposite side / hypotenuse

Replacing:

Sin85 = 33ft / h

Solve for h:

h= 33ft¨*sin 85

h= 32.87

The answer is 32.87