What are the angle measures of the triangle?

Question

asked Feb 1, 2018 157k views

2 Answers

Secureboot · Answer 1 · 2018-02-06T20:52:22+0000

Answer:

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

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

$(14√(3))^(2) =21^(2)+(7√(3))^(2)\\ \\588=441+147\\ \\588=588$

Is a right triangle

therefore

the measure of angle A is
$90\°$

Step 2

In the right triangle ABC

cos(C)=(21)/(14√(3))

$C=arcos((21)/(14√(3)))=30\°$

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
$30\°,60\°,90\°$