A triangle is shown, one angle labeled as 30 degrees and one side as 11 rad 3. Find the missing sides

Question

The adjacent side is 11 rad 3 te side opposite the 30 degree angle is labeled b and the hypotenuse is labelled a.

Answer 1

Presuming that by the expression 11 rad3 you meant 11√3, then we can calculate the answers.

 

Since you described one side of the triangle as "the hypotenuse" we have a right triangle.

The hypotenuse is side a, the side opposite the 30^o angle is b.

 

We know that the tangent of an angle is the opposite side ÷ adjacent side. Therefore, tangent 30^o = b ÷ 11√3

The tangent of 30^o = 0.57736. So, 0.57735 = b ÷ 11√3; then 0.57735 · 11√3 = b; b = 11

 

We know that the cosine of an angle is the adjacent side ÷ hypotenuse. Therefore, cosine 30^o = 11√3 ÷ a

The cosine of 30o = 0.866, so 0.866 = 11√3 ÷ a; a = 11√3 ÷ 0.866 = 22

 

We now have all three sides, so we can use the Pythagorean theorem to check our work. We know that a² = b² + c², so 22² = (11√3)² + 11², and we get 484 = 484