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# 19. Suppose a triangle with area 6 has sides of lengths 3 and 8. Find the angle between those two sides.?

Precalc

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- PuzzlingLv 72 months ago
When you have a triangle with two sides (a and b) and the included angle (C), the formula for the area is:

Area = ab sin(C) / 2

Plug in your values:

Area = 6

a = 3

b = 8

6 = 3*8 sin(C)/2

12 = 24 sin(C)

sin(C) = 0.5

C = arcsin(0.5)

C = 30° or 150°

Answer:

There are two equally valid answers.

C is 30° or 150°

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