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What is the value of b?
Round your answer to the nearest tenth.
15.7 yd
24.1 yd
35.1 yd
36.2 yd
The figure shows acute triangle A B C. The measure of angle B is 34 degrees. The length of side A B is 28 yard. The length of side B C is 22 yard. The length of side C A is b.

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MISSINGFile
Do do this problem, you need to use the Law of Cosines!

You are trying to find length b, so

b^2 = a^2 + c^2 - 2ab cos B
b^2 = 22^2 + 28^2 - 2(22)(28) cos 34
b^2 = 484 + 784 - 1232 cos 34
b^2 = 1268 - 1232 cos 34
b^2 = 246.6257
b = 15.7 yards

Hope this helps!

Answer:

A. 15.7 yards.

Step-by-step explanation:

Please find the attached file.

We have been given that in triangle ABC, the measure of angle B is 34 degrees. The length of side AB is 28 yards and the length of side BC is 22 yards. The length of side CA is b.

We will use law of cosines to find the length of side 'b'.

[tex]c^2=a^2+b^2-2ab\times cos(C)[/tex]

Upon substituting our given values in above formula we will get,

[tex]CA^2=22^2+28^2-2\times 22\times 28\times cos(34^{\circ})[/tex]

[tex]CA^2=484+784-1232\times 0.829037572555[/tex]

[tex]CA^2=1268-1021.37428938776[/tex]

[tex]CA^2=246.62571061224[/tex]

Taking square root of both sides we will get,

[tex]CA=\sqrt{246.62571061224}[/tex]

[tex]CA=15.70432139929\approx 15.7[/tex]

Since the length of side CA is b, therefore, the value of b is 15.7 yards and option A is the correct choice.

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