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In this 30°-60°-90° right triangle, the length of the long leg is 9√3

What is the measure of the hypotenuse n and the short leg m?
30°
9√3
n
m

User Cjquinn
by
7.3k points

2 Answers

4 votes

Answer:

9

Explanation:

In a 30°-60°-90° right triangle, the sides are always in the ratio of 1: √3:2, where 1 is the length of the short leg opposite the 30° angle, √3 is the length of the long leg opposite the 60° angle, and 2 is the length of the hypotenuse opposite the 90° angle1234.

In this case, we are given that the long leg is 9√3, so we can use this value to find the other sides by setting up a proportion:

short leglong leg​=13​​

short leg93​​=13​​

Cross-multiplying and solving for the short leg, we get:

short leg=3​93​×1​=9

Similarly, we can use another proportion to find the hypotenuse:

long leghypotenuse​=3​2​

93​hypotenuse​=3​2​

Cross-multiplying and solving for the hypotenuse, we get:

hypotenuse=3​2×93​​=18

Therefore, the measure of the hypotenuse n is 18 and the measure of the short leg m is 9.

User TexasEngineer
by
7.7k points
1 vote

Answer:

30°

Explanation:

User Ikari
by
7.6k points