Question

Solve the right triangle ABC with right angle C, if B=30 degrees, and C = 10

A.) a=5, b=5, A=60 degrees

B.) a=5, b=8.6602, A=60 degrees

C.) a=5.7735, b=11.5470, A=60 degrees

D.) a=8.6602, b=5, A=60 degrees

Answer 1

The answer to your question is letter D

Explanation:

We know that the sum of the internal angles in a triangle equals 180°.

So, B = 30°, C = 90° and A = ?

A + B + C = 180°

Substitution

A + 30 + 90 = 180

Solve for A

A = 180 - 30 - 90

A = 180 - 120

A = 60°

To find "b". use the trigonometric function sine

sin B =
`(opposite side)/(hypotenuse)`

sin B x hypotenuse = Opposite side

Opposite side = sin 30 x 10

Opposite side = 0.5 x 10

Opposite side = b = 5.0

To find "a" use the trigonometric function cosine

Cos A = adjacent side / hypotenuse

Adjacent side = a = cos A x hypotenuse

Adjacent side = a = cos 60 x 10

a = 0.866 x 10

a = 8.66