In ΔFGH, the measure of ∠H=90°, FH = 39, GF = 89, and HG = 80. What ratio represents the cotangent of ∠G?

Given:

In ΔFGH, the measure of ∠H=90°, FH = 39, GF = 89, and HG = 80.

To find:

The ratio which represents the cotangent of ∠G.

Solution:

In a right angle triangle, the ratio of the cotangent of an angle is

It is also written as

In ΔFGH, the measure of ∠H=90°. So,

Therefore, the ratio for the cotangent of ∠G is .

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,