Question

If cos(2/3(x) + 20) ° = sin(2x – 10)”, find the acute angles of the corresponding right triangle.

Answer 1

recall that

sin(x) = cos(90-x)

therefore

cos((2/3)x + 20) = cos(90 - [2x - 10])

(2/3)x + 20 = 100 - 2x

2x + (2/3)x = 80

divide through by 2

x + (1/3)x = 40

(4/3)x =40

4x = 40*3

4x = 120

x = 30

since it is a right angled triangle, the angles are 30, 60 and 90

Answer 2

Answer: A=40 B=50

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