Harley draws as triangle ABC, with the following measures: m∠B=90° and m∠A=30°. The hypotenuse of triangle ABC, AC has a length of 8√17 cm. What is the value of a (the length of BC)?

Answer 1

Since angle A is 30^o and angle B is 90^o, we have a 30-60-90 right triangle.

1. The side opposite the 30^o angle (BC) is a
2. The hypotenuse (AC) is 2a
3. the other side (AB) is a*sqrt(3)

We are given that AC = 2a = 8*sqrt(17). So what is a = BC = ___?

Answer 2

In a 30-60 right triangle, the shorter leg = half the hypotenuse.

The longer leg = the shorter leg times the square root of 3.

Since BC is across from the 30 degree angle, it is the shorter leg. AC is the hypotenuse.

Therefore, BC = 4 square root of 17