Answer:
106.5
Step-by-step explanation:
Trigonometric (trig) functions relate side lengths of a right triangle to the angle measures of the triangle. The mnemonic SOH CAH TOA is intended to help you remember the relationships. It is short for ...
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
In the given triangle, the side labeled x is the hypotenuse. The side labeled 50 is adjacent to the angle labeled 62°, so we could write the equation ...
cos(62°) = 50/x
The side labeled 50 is opposite the angle labeled 28°, so we could also write the equation ...
sin(28°) = 50/x
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Using either one of these equations will give you the same value for x.* Let's use the second:
x·sin(28°) = 50 . . . . . . multiply the above equation by x
x = 50/sin(28°) . . . . . . divide by the coefficient of x
Using a calculator, we can evaluate this expression to be ...
x ≈ 50/0.46947156
x ≈ 106.50272
The value of x is about 106.5.
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* The reason they both give you the same answer is cos(62°) = sin(28°).
