Sine, Cosine, Tangent

Question

Solve the triangle below without using either the cosine or tangent ratios. Show your work.

1. 

Answer 1

Missing angle B:

For triangles: A + B + C = 180°

B = 180° - A - C

B = 180° - (23°) - (90°)

B = 67°

Missing sides a and b:

Law of Sines: a/sinA = b/sinB = c/sinC

So a = c*sinA/sinC, b = c*sinB/sinC

a = (16)*sin(23°)/sin(90°), b = (16)*sin(67°)/sin(90°)

a = 6.3, b = 14.7

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Answer 2

a = 16sin23° ≈ 6.25 ≈ 6.

Then by Pytagorian theorem b ≈ 16² - 6²)^1/2 ≈ 15.

B = 90° - 23° = 67°

Answer 3

a = 16 sin 23°

b = 16 sin 67°