Question

In ΔA B C, ∠B is a right angle, A B=30 , and secA= 5/3 . Find each value in fraction and in decimal form.

tan C

Answer 1

`\sec A=(AC)/(AB) \implies (AC)/(30)=(5)/(3) \implies AC=50`

By the Pythagorean theorem,
`BC=√(50^2-30^2)=40`.

So, it follows that:

`\tan C=(AB)/(BC)=(30)/(40)=\boxed{(3)/(4)}`