Question

What are the angle measures of the triangle?

Answer 1

A. 30,60,90 Can't see p

Answer 2

Answer:

The measures of the triangle are $30\°,60\°,90\°$

Step-by-step explanation:

see the attached figure with letters to better understand the problem  

Step 1

Verify if the triangle ABC is a right triangle

Applying the Pythagoras Theorem

$(14\sqrt{3})^{2} =21^{2}+(7\sqrt{3})^{2}\\ \\588=441+147\\ \\588=588$

Is a right triangle

therefore

the measure of angle A is $90\°$

Step 2

In the right triangle ABC

$cos(C)=\frac{21}{14\sqrt{3}}$

$C=arcos(\frac{21}{14\sqrt{3}})=30\°$

Step 3

Find the measure of angle B

we know that

the sum of the internal angles of a triangle is equal to $180\°$

so

$A+B+C=180\°$

substitute the values and solve for B

$90\°+B+30\°=180\°$

$B+120\°=180\°$

$B=60\°$

The measures of the triangle are $30\°,60\°,90\°$