Question

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

Answer 1

We are given

`tan(A)=(7)/(24)`

we know that

`tan(A)=(opposite)/(adjacent)`

so, we get

opposite =7

adjacent=24

now, we can find hypotenuse

`hypotenuse=√(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)=(adjacent)/(hypotenuse)`

In second triangle:

adjacent=7

hypotenuse =25

so, we get

`cos(B)=(7)/(25)`................Answer