Answer:
x° ≈ 77.6°
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relationships between trig functions and triangle sides. Side CD is common to the triangle on the left and the one on the right, so we can consider relationships that might help us use that to find the answer.
In the triangle on the right, we need a relationship between CD and BD. These sides are opposite and adjacent to the given angle, so we can use the relation ...
Tan = Opposite/Adjacent
tan(38°) = CD/3.5
Multiplying by 3.5, we can find CD:
CD = 3.5·tan(38°)
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In the triangle on the left, we know sides CD and CA, the side opposite x° and the hypotenuse of that right triangle. This lets us use the sine relationship:
Sin = Opposite/Hypotenuse
sin(x°) = CD/2.8
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Using our value for CD, this becomes ...
sin(x°) = (3.5·tan(38°)/2.8)
sin(x°) = (5/4)tan(38°)
Using the inverse sine function, we can find x° to be ...
x° = arcsin(5/4·tan(38°)) ≈ 77.6°
The size of the angle marked x° is about 77.6°.
