Question

Which set of values could be the side lengths of a 30-60-90 triangle?

Answer 1

B.
`(5,5√(3),10)`

Explanation:

Since we know that in 30-60-90 triangle, the side corresponding to angle 90 degrees is two times the length of side corresponding to 30 degree angle. The length of side corresponding to 60 degree angle is
`√(3)` times the length corresponding to 30 degree angle.

We can see from our given choices that the side corresponding to 30 degree angle is 5 units.

`\text{The side corresponding to 60 degree angle}=√(3)* 5`

`\text{The side corresponding to 60 degree angle}=5√(3)`

`\text{The side corresponding to 90 degree angle}=2* 5`

`\text{The side corresponding to 90 degree angle}=10`

Therefore, the side lengths of a 30-60-90 triangle will be
`(5,5√(3),10)` and option B is the correct choice.