Answer:
75
Step-by-step explanation:
The mnemonic SOH CAH TOA is intended to remind you of the relationship between trig functions of angles in a right triangle, and the sides of that triangle. Here, we need to apply two different trig functions to find the value of x.
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altitude
The altitude of the larger acute triangle is the side adjacent to the 35° angle. The side opposite that angle is shown as 39. The relevant relation is ...
Tan = Opposite/Adjacent
tan(35°) = 39/altitude
Solving for altitude, we get ...
altitude = 39/tan(35°) ≈ 55.698
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x
The side marked x is the hypotenuse of the triangle with angle 42°. The side adjacent to that angle is the altitude that we just found. Then the relevant trig relation is ...
Cos = Adjacent/Hypotenuse
cos(42°) = altitude/x
Solving for x, we get ...
x = altitude/cos(42°) = (39/tan(35°))/cos(42°)
x = 39/(tan(35°)cos(42°)) ≈ 74.949
The value of x is about 75.
