Angles A and B are complementary. If sin A = 4x + 10 and cos B = 2x + 16, what is the value of x?Option- 313422

AlbertM asked Apr 21, 2023

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AlbertM asked Apr 21, 2023

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24 votes

We have that A and B are complementary, therefore their sum is equal to 90°. If ∠A and ∠B are complementary angles, this is:

$\sin A=\cos B$

Where:

sin A = 4x + 10

cos B = 2x + 16

Substitute the values:

And solve for x:

$\begin{gathered} 4x+10-2x=2x+16-2x \\ 2x+10=16 \\ 2x+10-10=16-10 \\ 2x=6 \\ (2x)/(2)=(6)/(2) \\ x=3 \end{gathered}$

Answer: x = 3

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