Question

ΔABC is a right triangle and ∠B is a right angle. If sin ∠A = 3/5, then what is the ratio for tan ∠C?

Answer 1

4/3

Explanation:

The right triangle is a 3-4-5 triangle- the opposite side of a is 3 (based on 3/5 which is opp/hyp) and the hypnotuse is 5. The ohter side is 4 no matter how it is solved individually. For tan, it is opp/adj so the opp of angle c is 4 and the adj is 3. Therefore it is 4/3. :D The other person flipped it.

Answer 2

`Tan \ \angle C=(3)/(4)`

Explanation:

-The sine of an angle in a right triangle is given as:

`Sin \ \theta=(Opposite)/(Hypotenuse)\\\\\therefore Sin \ \angle A=(3)/(5)`

-From this Trigonometric ratio, we calculate the length of the adjacent as:

`b^2+h^2=H^2\\\\b^2=5^2-3^2\\\\b^=4\\\\\therefore Adjacent=4`

We then calculate tan ∠C

`Tan \ \ theta=(Opposite)/(Adjacent)\\\\Tan \ \angle C=(3)/(4)`