SOLUTION: What are the angle measure of the triangle if the measures are 21, 7 sqrt 3, and 14 sqrt 3?

Question 1152046: What are the angle measure of the triangle if the measures are 21, 7 sqrt 3, and 14 sqrt 3?
Found 3 solutions by Boreal, MathLover1, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
My approach to this is to note that 7 sqrt(3) is half of 14 sqrt (3), and this is probably going to be a 1-2-sqrt(3) 30-90-60 right triangle
Sure enough, 7 sqrt(3) *sqrt(3)=21
30-60-90 degree right triangle.

Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
What are the angle measure of the triangle if the measures are

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Angle ∠ ° = °'"....round it
Angle ∠ °

Angle ∠

Angle ∠

Angle ∠

Angle ∠ rad
Angle ∠ ° = °'"......round it
Angle ∠ °

Angle ∠

Angle ∠

Angle ∠

Angle ∠ rad
Angle ∠ ° = °'"......round it

Angle ∠ °

Answer by ikleyn(52792)   (Show Source): You can put this solution on YOUR website!
.
What are the angle measures of the triangle? the sides are 21, 7 sqrt 3 and 14 sqrt 3
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            Please notice on how I edited your post in order for to make sense.

Solution

Notice that + = 49*3 + 441 = 147 + 441 = 588= 3*196 = = . Thus the triangle with the side lengths of 21, and is a right angled triangle with the legs 21 and and the hypotenuse of . Also, the leg is half length of the hypotenuse . Therefore, the given triangle is (30°, 60°, 90°)- triangle. Its angles are 30°, 60° and 90°.

Solved.

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