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2. In AABC, m < B = 22°, m < C = 52° and a = 30. Find the length of b to the nearest tenth.

Sagot :

jfb14439

Answer:

232

Step-by-step explanation:

Answer:  11.7

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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.

View image jimthompson5910
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