Question

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

Answer 1

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

`\cot \theta =(Base)/(Perpendicular)`

It is also written as

`\cot \theta =(Adjacent)/(Opposite)`

In ΔFGH, the measure of ∠H=90°. So,

`\cot G =(HG)/(FH)`

`\cot G =(80)/(39)`

Therefore, the ratio for the cotangent of ∠G is
`\cot G=(80)/(39)`.