Answer:
6.2 units
Step-by-step explanation:
The mnemonic SOH CAH TOA is intended to remind you of the relations between trig functions and sides of a right triangle.
Common segment
To find the value of x in this figure, we need to know the length of the common segment between the two triangles. That segment is opposite the 53° angle, so can be found using the sine relation:
Sin = Opposite/Hypotenuse
Opposite = Hypotenuse × Sin = 30·sin(53°) ≈ 23.9591
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Missing measure
The side marked x is adjacent to the marked angle in that triangle, so the relevant relation is ...
Cos = Adjacent/Hypotenuse
Adjacent = Hypotenuse × Cos = 23.9591·cos(75°) ≈ 6.20106
The length of the side marked x is about 6.2 units.
