Question

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

ANSWERS
square root of fifteen divided by eight
eight divided by the square root of fifteen
seven divided by the square root of fifteen
square root of fifteen divided by seven

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