A 30°-60°-90° triangle has a hypotenuse with a length of 10. What is the length of the longer leg of the triangle?

This is a SPECIAL RIGHT TRIANGLE...you should have learned about two SPECIAL RIGHT TRIANGLES...

30 - 60 - 90
and
45 - 45 - 90

the RATIO OF THE SIDES OF A 30 - 60 - 90 right triangle are ALWAYS:

1 : √3 : 2

the shorter leg is (1/2) the length of the hypotenuse
the longer leg is (√3) times greater than the shorter leg

the answer is: 5√3 units

what is the ratio of the sides for a 45 - 45 - 90 right triangle ? Don't you read your textbook ??

Ω

2 / sqrt ( 3 ) = 10 / x
x = ( 10 / 2 ) * sqrt 3
x = 5 sqrt 3

B) 5 * sqrt(3)

One length is: 10*sin(30) = 10 * 0.5 = 5
One length is: 10*cos(30) = 10 * (sqrt(3)/2)) = sqrt(75) = sqrt(25)*sqrt(3) = 5*sqrt3)

OR
One length is: 10*sin(30) = 10 * 0.5 = 5
x^2 = 10^2 - 5^2
x^2 = (100-25)
x = sqrt(75)
x = sqrt(25)*sqrt(3)
x = 5 * sqrt(3) which is bigger/longer than 5.

30-60-90 triangle has sides in proportion 1:2:SQR(3)
If the hypotenuse is 10, the longer leg is 5SQR(3)
Choice (B)