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

1. A

2. C

Explanation:

Answer 2

See explanation

Explanation:

Definitions:

`\sin x=\frac{\text{opposite leg}}{\text{hypotenuse}}\\ \\\tan x=\frac{\text{opposite leg}}{\text{adjacent leg}}`

Hence,

`\sin B=(b)/(a)\\ \\\tan C=(c)/(b)\\ \\\sin B\cdot \tan C=(b)/(a)\cdot (c)/(b)=(c)/(a)`

and

`\sin C=(c)/(a)\\ \\\tan B=(b)/(c)\\ \\\sin C\cdot \tan B=(c)/(a)\cdot (b)/(c)=(b)/(a)`