Question

An acute angle θ is in a right triangle with sin θ = seven eighths. What is the value of cot θ?

Answer 1

Draw a right triangle ABC, with m(CAB)=∅.

Let CB=7 units, AC=8 units, so by the Pythagorean theorem:

$AB= \sqrt{ AC^{2} - BC^{2} }= \sqrt{ 8^{2} - 7^{2} }= \sqrt{64-49} = \sqrt{15}$ (units)

so we have drawn a triangle where sin∅=7/8

in this triangle, cot∅=(adjacent side)/(opposite side)=$\frac{ \sqrt{15} }{7}$

Answer: square root of fifteen divided by seven