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21) Find the measure of angle A. of the oblique triangle ABC if side ABC is 3 ft, side BC is 2ft, and the included angle B is 30 degrees

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A. 38.2

Step-by-step explanation:

a=2 c=3 B=30

first use law of cosines

to get the third side

3rd side is 1.61

then use law of sines

to get the angle in question

law of cosines is square root of (c=a2+b2﹣2abcosB)

square root of (2^2+3^2﹣2·2·3·cos(30°))≈1.61484

then law of sines

law of sines a=b×(sinα/sinβ)

sin-1 means arc sine

β=sin-1(sinα·b/a)

sin-1(sin(30°)·2/1.61) = sin-1(sin(30°)·2/1.61) = sin-1(0.62) = 38.2

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