Trigonometry Question

Question

A 5 foot tall hiker stands on top of a cliff. She looks down to see her campsite in the valley below. The angle of depression is 12.8 degrees. The hiker knows that her campsite is 120 feet away from the base of the cliff. How tall is the cliff where the hiker is standing: Answer

ROUND TO THE NEAREST TENTH 

Answer 1

since the distance from the cliff was given as 120 feet and an angle was provided, as the angle of depression, as 12.8 with the objective of this problem being to find the cliff height from the campsite to the hiker then the sin of the angle of 12.8 must be what we are working with. so the problem is set up like this.

sin(12.8)=x/120 where x is the opposite side of this ratio with 120 being the hypotenuse or distance from the hiker to the campsite. to find x 120 must be multiplied on both sides like this. sin(12.8) x 120=(x/120)120. since 120 is dividing x; multiplying 120 will undo the operation. This only seems to work for the denominator only because it is the part that is dividing the numerator if a fraction is represented as a division problem. Then multiply 120 by sin(12.8) and the answer will be 26.58581971 or rounding to the nearest tenth will be 26.6 or hundredth will be 26.59.