Question

PLS ANSWER THIS ASAP!!!!

Eric leans a ladder against the roof of his house so that the ladder forms a 70° angle with the ground. The roof of the house is 13 feet above the ground. How far is the bottom of the ladder from the base of the house? Round the answer to the nearest tenth.


A.

0.2 feet

B.

4.4 feet

C.

4.7 feet

D.

71.2 feet

Answer 1

The answer is not listed. The correct answer is 10.6 feet.

Explanation:

This problem is solved by using the tangent.

Using the triangle shown in the picture, we can label the sides as the hypotenuse (across from the right angle), the opposite (opposite from the 70 degree angle) and adjacent (last remaining side, adjacent to the 70 degree angle).

Using the formula for tangent (tangent = opposite/adjacent), we can plug in the numbers: tan(70) = 13/x

To simplify this, multiply both sides by x: (x)tan(70) = 13/x (x)

The x's on the right cancel each other out, leaving you with: (x)tan(70) = 13

To isolate the variable, x, divide both sides by tan(70): tan(70)/(x)tan(70) = 13/tan(70)

The tan(70)'s cancel each other out on the left side, leaving you with: x = 13/tan(70)

Plug this into your calculator to get: 10.63864682...

Round to the nearest tenth and get: 10.6