Question

I now have another question to ask.

A ladder that is 26 ft long leans against a building, making a 65 degree angle of elevation with the ground.
To the nearest tenth of a foot, how far up the building does the ladder reach?

Answer 1

23.6 ft

Explanation:

Sketch a right triangle representing this situation. The length of the hypotenuse is 26 ft and the angle of elevation from ground to top of ladder is 65°. The "opposite side" is the reach of the ladder, which we'll call x.

Then:

opp

• sin 65° = ----------
• 26 ft

or (26 ft)(sin 65°) = opp side = height off the ground of top of ladder.

Evaluating this, we get:

(26 ft)(0.906) = 23.56 ft, or, rounded off, 23.6 ft

The ladder reaches 23.6 ft up the side of the building.