Question

In △ABC,c=12, m∠B=27°, and a=9. Find b.

A. 11.5
B. 13.2
C. 6.8
D. 5.7

Answer 1

D. 5.7

Explanation:

We have been given that in △ABC,c=12, m∠B=27°, and a=9. We are asked to find the value of b.

We will use law of cosines to solve for b.

`b^2=a^2+c^2-2ac\cdot \tect{cos}(B)`

Upon substituting our given values in law of cosines, we will get:

`b^2=9^2+12^2-2\cdot 9\cdot 12\cdot {cos}(27^(\circ))`

`b^2=81+144-216\cdot 0.891006524188`

`b^2=225-192.457409224608`

`b^2=32.542590775392`

Now, we will take square root of both sides of our equation.

`b=√(32.542590775392)`

`b=5.70461136059`

`b\approx 5.7`

Therefore, the value of b is 5.7 and option D is the correct choice.

Answer 2

Option D is correct.

Explanation:

We are given c = 12

m∠B = 27°

a = 9

We need to find b

We would use Law of Cosines

`b = a^2 + c^2 -2ac\,cosB`

Putting values and solving

`b^2 = (9)^2 + (12)^2 -2(9)(12)\,cos(27°)\\b^2 = 81 + 144 - 216(0.891)\\b^2 = 81 + 144 - 192.456\\b^2 = 32.54\\taking\,\,square\,\,roots\,\,on\,\,both\,\,sides\\\\√(b^2) = √(32.54)\\ b = 5.7`

So, Option D is correct.