Question

Determining angle side relationships What are the angle measures in trainable ABC?

Answer 1

m∠A=90°, m∠B=60°, m∠C=30°

Explanation:

step 1

Verify if the triangle ABC is a right triangle

Applying the Pythagoras theorem

`12^(2)=6^(2)+(6√(3))^(2)`

`144=144` ----> is true

therefore

Is a right triangle

m∠A=90°

Find the measure of angle C

sin(C)=AB/BC

substitute

sin(C)=6/12=1/2

so

m∠C=30°

Find the measure of angle B

we know that

m∠C+m∠B=90°------> by complementary angles

so

m∠B=90°-30°=60°