Alexandra needs to reshingle her roof. She leans a ladder against the the wall of the house so that the top of the ladder is 8 feet above the ground. The bottom of the ladder is 5 feet from the base of the wall. Find the angle formed between the ladder and the house. Round the answer to the nearest whole degree.

Alexandra needs to reshingle her roof. She leans a ladder against the the wall of the house so that the top of the ladder is 8 feet above the ground. The bottom of the ladder is 5 feet from the base of the wall. Using trigonometric ratios, the angle formed between the ladder and the house is 32°.

What is trigonometric ratios?

Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle. The basic trigonometric ratios are sin, cos, and tan, namely sine, cosine, and tangent ratios. The other important trigonometric ratios, cosec, sec, and cot, can be derived using the sin, cos, and tan respectively.

What is tangent of an angle?

the tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

Height of the wall = 8 feet

Distance between base of wall and ladder = 5 feet

Angle between the ladder and the house = a

Then, the tangent of angle a is given by

tan a = [tex]\frac{perpendicular}{base} =\frac{5}{8} = 0.625[/tex]

a = [tex]tan^{-1}(0.625) = 32[/tex]

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