Question

Solve the given triangle. Round the measures of sides to the nearest tenth and measures of angles to the nearest degree. c = 8, B = 50°, C = 55°

Question 15 options:


A. A = 75°, a = 63.6, b = 7.5

B. A = 75°, a = 7.5, b = 9.4

C. A = 75°, a = 9.4, b = 7.5

D. A = 75°, a = 8, b = 7.5

Answer 1

C. A = 75°, a = 9.4, b = 7.5 is correct.

Explanation:

Answer 2

A =
`75^o`, a = 9.4 , and b = 7.5 (which coincides with option C among the listed possible answers)

Explanation:

First, we can find the length of side b through the law if sines:

`(b)/(sin(B)) = (c)/(sin(C))\\b=(c\,*\,sin(B))/(sin(C))\\ b=(8\,*\,sin(50^o))/(sin(55^o))\\b=7.481`

That we can round to 7.5

Now we can find angle A using the property that the addition of all angles in a triangle must equal
`180^o`:

`A+B+C=180^o\\A+50^o+55^o=180^o\\A=180^o-50^o-55^o\\A=75^o`

And finally, we can find side "a" by using again the law of sines:

`(a)/(sin(A)) = (c)/(sin(C))\\a=(c\,*\,sin(A))/(sin(C))\\ a=(8\,*\,sin(75^o))/(sin(55^o))\\a=9.4334`

which can be rounded to a = 9.4