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

$\cot \theta =\dfrac{Base}{Perpendicular}$

It is also written as

$\cot \theta =\dfrac{Adjacent}{Opposite}$

In ΔFGH, the measure of ∠H=90°. So,

$\cot G =\dfrac{HG}{FH}$

$\cot G =\dfrac{80}{39}$

Therefore, the ratio for the cotangent of ∠G is $\cot G=\dfrac{80}{39}$.