Question

A 10-foot ladder is placed against a building so that the ladder makes a 78º angle with the ground. To the nearest tenth of a foot, at what height does the ladder touch the building?
A. 7.8 ft

B. 9.8 ft

C. 10.2 ft

D. 16.2 ft

Answer 1

Step-by-step explanation:

law of sine :

a/sinA = b/sinB = c/sinC

with the sides and the associated angles being opposite in the triangle.

the angle opposite to the ladder is the right angle.

the height of the ladder touch point is opposite of the 78° angle.

so, we get

10/sin(90) = height/sin(78)

10/1 = height/sin(78)

10 = height/sin(78)

height = 10×sin(78) = 9.781476007... ft ≈ 9.8 ft

so, B is the right answer