Find the remaining sides of a 30° - 60° - 90° triangle if the side opposite 60° is 18.
A) ,
B) ,
C) ,
D) ,
E) ,

Question

Find the remaining sides of a 30° - 60° - 90° triangle if the side opposite 60° is 18.
A) , 
B) , 
C)​ , 
D) , 
E) ,

Quizplus · Accepted Answer

In a 30°-60°-90° triangle, the side opposite the 30° angle is half the length of the hypotenuse (which is the side opposite the 90° angle), and the side opposite the 60° angle is √3 times the length of the side opposite the 30° angle.

Therefore, in this triangle, the hypotenuse is 2(18) = 36, and the side opposite the 30° angle is 18/2 = 9.

The side opposite the 60° angle is √3 times the side opposite the 30° angle, so it is √3(9) = 9√3.

Thus, the remaining sides of the triangle are 9 and 9√3.

Therefore, the answer is B, (11ebf5ef_bb55_e7bd_95d1_8d6985153750_TBX9354_11,11ebf5ef_bb55_e7be_95d1_93e965c0128b_TBX9354_11).

Find the Remaining Sides of a 30° - 60° - 90° Triangle If