71.9k views
1 vote
Which set of values could be the side lengths of a 30-60-90 triangle?

OA. (5, 5√2, 10}
B. (5, 10, 10 √√3)
C. (5, 10, 102)
OD. (5, 53, 10)

User GodEater
by
8.5k points

1 Answer

5 votes

A 30-60-90 triangle is a special type of right triangle where the angles are 30 degrees, 60 degrees, and 90 degrees. The sides of a 30-60-90 triangle always have the same ratio, which is 1 : √3 : 2.

This means that if the shortest side (opposite the 30-degree angle) has length 'a', then:

- The side opposite the 60-degree angle (the longer leg) will be 'a√3'.

- The side opposite the 90-degree angle (the hypotenuse) will be '2a'.

Let's check each of the options:

A. (5, 5√2, 10): This does not follow the 1 : √3 : 2 ratio.

B. (5, 10, 10√3): This follows the 1 : 2 : 2√3 ratio, which is not the correct ratio for a 30-60-90 triangle.

C. (5, 10, 10^2): This does not follow the 1 : √3 : 2 ratio.

D. (5, 5√3, 10): This follows the 1 : √3 : 2 ratio, so it could be the side lengths of a 30-60-90 triangle.

So, the correct answer is option D. (5, 5√3, 10).

User Kunal Panchal
by
8.9k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories