Question

Suppose there is a triangle with sides a, b, and c and angles A, B, and C. Using the known given information below and the law of cosines, what is the measure of angle B? Round your answer to the nearest whole number, if necessary.a = 14 cmb = 9 cmc = 6 cm

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

data:

triangle:

sides:

a = 14 cm

b = 9 cm

c = 6 cm

Step 02:

law of cosines:

`b^2=a^2+c^2-2(a)(c)\text{ cos B }`
`(9\text{ cm\rparen}^2=(14\text{ cm\rparen}^2+(6\text{ cm\rparen}^2-2(14\text{ cm})(6\text{ cm})\text{ cos B }`
`-151\text{ cm}^2=-2(14\text{ cm})(6\text{ cm})\text{ cos B }`
`0.8988=\text{ cos B }`

B = arc cos 0.8988

B = 25.99

The answer is:

B = 26°