Question

In the right triangle shown, \angle A = 30^\circ∠A=30∘angle, A, equals, 30, degrees and AB = 8AB=8A, B, equals, 8.

How long is BCBCB, C?
Answer exactly, using a radical if needed.​

Answer 1

Answer:

BC=4 units

Step-by-step explanation:

The picture of the question in the attached figure

we know that

In the right triangle ABC

$sin(A)=\frac{BC}{AB}$ ----> by SOH (opposite side divided by the hypotenuse)

we have

$AB=8\ units\\A=30^o$

substitute the given values

$sin(30^o)=\frac{BC}{8}$

solve for BC

$BC=sin(30^o)(8)$

Remember that

$sin(30^o)=\frac{1}{2}$

so

$BC=(\frac{1}{2})(8)=4\ units$