2. In AABC, m < B = 22°, m < C = 52° and a = 30. Find the length of b to the nearest tenth.
2 answers:
<h3>Answer: 11.7</h3>
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Explanation:
I recommend drawing out the triangle. See below.
Notice how each lowercase letter is a side length, and the uppercase letters are angles. Also, each lowercase letter is opposite their corresponding uppercase counterpart.
- side a is opposite angle A
- side b is opposite angle B
- side c is opposite angle C
We're given that angles B and C are 22 degrees and 52 degrees in that order. Let's use the fact that the three angles of any triangle must add to 180 to solve for angle A
A+B+C = 180
A+22+52 = 180
A+74 = 180
A = 180-74
A = 106
We do this so we can then apply the law of sines
sin(A)/a = sin(B)/b
sin(106)/30 = sin(22)/b
b*sin(106) = 30*sin(22) ....... cross multiplication
b = 30*sin(22)/sin(106)
b = 11.6910908340182 ....... which is approximate
b = 11.7
Make sure your calculator is in degree mode.
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