What is the measurement needed of the third side of a triangle with two sides of 7 m and 14 m to make it a 30°, 60°, 90° triangle?
A)4.04 m
B)9.90 m
C)12.12 m
D)3.5 m

Question

Quizplus · Accepted Answer

In a 30°, 60°, 90° triangle, the ratio of the sides is 1:√3:2. 
So, if the shorter leg (opposite the 30° angle) is 7 m, the longer leg (opposite the 60° angle) will be 7√3 m (7 times the square root of 3). 
To find the length of the hypotenuse (opposite the 90° angle), we multiply the length of the shorter leg by 2, which gives us 14 m.
Therefore, if we subtract the square of the shorter leg from the square of the longer leg and take the square root of the result, we get the length of the missing side. 
c = √(14^2 - 7^2) 
c = √147 
c = 12.12 m 
Thus, the answer is C.

What Is the Measurement Needed of the Third Side of a Triangle