Question

Type the correct answer in each box. If necessary, use / for the fraction bar(s).

In this triangle, the product of sin B and tan C is ______
, and the product of sin C and tan B is _______

Answer 1

Answer:

See explanation

Step-by-step explanation:

Definitions:

$\sin x=\dfrac{\text{opposite leg}}{\text{hypotenuse}}\\ \\\tan x=\dfrac{\text{opposite leg}}{\text{adjacent leg}}$

Hence,

$\sin B=\dfrac{b}{a}\\ \\\tan C=\dfrac{c}{b}\\ \\\sin B\cdot \tan C=\dfrac{b}{a}\cdot \dfrac{c}{b}=\dfrac{c}{a}$

and

$\sin C=\dfrac{c}{a}\\ \\\tan B=\dfrac{b}{c}\\ \\\sin C\cdot \tan B=\dfrac{c}{a}\cdot \dfrac{b}{c}=\dfrac{b}{a}$

Answer 2

Answer:

1. A

2. C

Step-by-step explanation: