Answer:
Step-by-step explanation:
The place to start is ...
- read and understand the question
- understand the given information
After that, the next step is to make use of the relationships you know between the items of information given and those asked for.
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The first box you're asked to fill is the value of the third angle of the triangle. You know A is 30° because that's the way it is marked. You know C is 90° because it has the right-angle symbol there, and a right angle measures 90°. You know the sum of the three angles in any triangle is 180°, so you have ...
30° +90° +∠B = 180°
Subtracting 120° from both sides of this equation gives us ...
∠B = 60°
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Comment on this answer
It should also be pretty obvious that ∠B is the complement of ∠A in a right triangle. That is ...
30° +∠B = 90° . . . . . subtracting 90° from both sides of the above equation
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The second box you're asked to fill in is the length of the side opposite the given angle. You know this is a right triangle, so you know the definitions of the trig ratios apply. The mnemonic SOH CAH TOA reminds you of the sine relation:
Sin = Opposite/Hypotenuse
In this triangle, that means ...
sin(30°) = a/8
Multiplying by 8, we get ...
a = 8·sin(30°) = 8·1/2
a = 4
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The same mnemonic makes reference to the adjacent side, which is side b of the triangle. That is the measure asked for in the third box.
Cos = Adjacent/Hypotenuse
cos(30°) = b/8
Multiplying by 8, we get ...
b = 8·cos(30°) = 8·0.866025 ≈ 6.92820
b ≈ 6.93
