Answer:
The measures of the triangle are [tex]30\°,60\°,90\°[/tex]
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
[tex](14\sqrt{3})^{2} =21^{2}+(7\sqrt{3})^{2}\\ \\588=441+147\\ \\588=588[/tex]
Is a right triangle
therefore
the measure of angle A is [tex]90\°[/tex]
Step 2
In the right triangle ABC
[tex]cos(C)=\frac{21}{14\sqrt{3}}[/tex]
[tex]C=arcos(\frac{21}{14\sqrt{3}})=30\°[/tex]
Step 3
Find the measure of angle B
we know that
the sum of the internal angles of a triangle is equal to [tex]180\°[/tex]
so
[tex]A+B+C=180\°[/tex]
substitute the values and solve for B
[tex]90\°+B+30\°=180\°[/tex]
[tex]B+120\°=180\°[/tex]
[tex]B=60\°[/tex]
The measures of the triangle are [tex]30\°,60\°,90\°[/tex]
