Question

In right triangle ABC, ∠A is a right angle and sinC=35. What is the ratio for tanC? Enter your answer as the fraction, in simplest terms, like this: 42/53 (Look at the attached image)

Answer 1

tan(C) = 3/4

Explanation:

If the sine of angle C is 3/5 and we want to find the tangent of the angle C, we can first find the cosine of angle C using the following equation:

`sin^2(C) + cos^2(C) = 1`

`(3/5)^2 + cos^2(C) = 1`

`cos^2(C) = 1 - 9/25`

`cos^2(C) = 16/25`

`cos(C) = 4/5`

Then, we can find the tangent relation using the equation:

`tan(C) = sin(C) / cos(C)`

`tan(C) = (3/5) / (4/5)`

`tan(C) = 3/4`