can you help me on a geometry problem?

Question

A ladder is leaning against the side of a building. The ladder is 30 feet long, and the angle between the ladder and the building is 15°. About how far is the foot of the ladder from the building?

how would i do that step by step

Answer 1

This is a sine problem. The ladder forms the hypotenuse, while the side opposite the 15° angle is the value you are seeking.

sine = side opposite / hypotenuse

Let x = distance ladder base is from bldg.

sin 15 = x/30

x = 30 * sin 15

x = 7.76 ft or 7 ft 9.1 in
.

Answer 2

I always draw pictures. So draw your house, ladder and angle. Then use Pythagoras' law to work out the measurements.

The wall to the ground is 90 degrees, the angle at the top roof edge is 15, so the angle at the ground level is 180 - (15 + 90). The ladder is 30 ft tall.

I cannot do the math, but the principle is there.

Answer 3

ok so if you have learned cosine, sine, and tangent this is how to do it. the ladder, the building, and the ground form a right angel (the angel that the building hits the ground). In this case you would use sine. sin(15) = opposite side/ hypotenuse. the number in parenthesis is the angel measure. so then you just do: sin(15)= X/30. X=the side you're looking for. oh by the way you need a scientific or graphing calculator to do this. then the answer comes out to be 7.76 ft.