Triangle Question..

Question

A ladder is leaning against a building. The base of the ladder is 6 feet away from the building, and the angle formed by the ladder and the ground is 73 degrees. To the nearest tenth of a foot, how high up the building does the ladder reach?

 

Please show all steps taken to find the answer.

The following answers are provided as choices:

A.) 6 feet

B.) 19.6 feet

C.) 20.5 feet

D.) None of the above

Answer 1

B.) 19.6 feet.

Draw a right triangle ABC. AB will represent the ladder, with point A being on the ground and point B being against the building.

 

Label: AC=6 ft,  m<A=73° and <C is a right angle. 

 

Use the trig mnemonic "SOHCAHTOA" to identify that BC/AC=tan<A. So BC, which is the height the ladder reaches, equals AC*tan<A=6*tan(73)=19.6 feet.

 

Jeff

Answer 2

Hi Brook,

The tangent function will help to work this problem. Tan is opposite side divided by adjacent side for the 73° angle.

tan 73°= x/6ft

x = 6 tan 73° = 19.625ft so your answer is (C).