Question

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

Answer 1

part 1 = c/a

part 2 = b/a

Sine is the ratio of opposite to hypotenuse respect to as a given angle while tangent is the ratio of opposite to adjacent lengths of a given angle.

Part 1

Sine = opposite/hypotenuse

SinB = b/a

Tangent = opposite/adjacent

TanC = c/b

SinB × TanC = b/a×c/b

= c/a

Part 2

SinC = c/a

TanB = b/c

SinC×TanB= c/a×b/c

= b/a

Answer 2

In this triangle, the product of sin B and tan C is c/a or cos B, and the product of sin C and tan B is b/a cos C. We determine these as follows:

sin B tan C = b/a (c/b) = c/a

sin C tan B = c/a (b/c) = b/a

Hope this answers the question. Have a nice day.