Question

Given \tan A = \frac{7}{{24}}, find the cos B

Answer 1

We are given

$tan(A)=\frac{7}{24}$

we know that

$tan(A)=\frac{opposite}{adjacent}$

so, we get

opposite =7

adjacent=24

now, we can find hypotenuse

$hypotenuse=\sqrt{7^2+24^2}$

$hypotenuse=25$

now, we can draw triangle and then switch vertices accordingly

we can find cos(B) using second triangle

$cos(B)=\frac{adjacent}{hypotenuse}$

In second triangle:

adjacent=7

hypotenuse =25

so, we get

$cos(B)=\frac{7}{25}$................Answer