another 30-60-90 geometry question?

Question

The hypotenuse of a 30-60-90 triangle has length 15. What is the length of the side opposite the 60 angle? If necessary, round your answer to two decimal places.

Answer 1

Well this is half an equilateral triangle So the length of the side next to the 60 angle other than the hypotenuse is 15/2 ie 7.5

By Pythagoras' Rule

side² = 15² - (7.5)²
= 7.5²(2² - 1²)

= 56.25 * 3

= 168.75

So side = √(168.75)
≈ 12.99

Answer 2

There are a couple of ways you can do this - I think the trig solution is easiest. For right triangles, sin (x) = opposite/hypotenuse. We want to know the side opposite the 60 degree angle, so we plug in 60 for the x (the angle), and 15 for the hypotenuse:

sin(60) = opposite/15
15 * sin(60) = opposite
opposite ~ 12.99

You could also use the known ratio of sides for 30-60-90 triangles and set up a proportion to solve. The "30-60-90 triangle" has sides in the ratio of 1: sqrt(3) : 2, respectively. So you could set up:
sqrt(3) / 2 = x / 15
Solve for x, and you get the same result.

Answer 3

A 30-60-90 triangle is 1/2 of an equilateral triangle. That makes the shortest side equal to 1/2 of the hypotenuse. The 3rd side can now be calculated using the Pythagorean theorem.

Answer 4

In a 60-30-90 triangle, the side opposite the thirty degree angle is always half the hypotenuse. So the side opposite the thrity degree angle is 7.5. To get the side opposite the 60 degree side, you multiply 7.5 by the square root of three. This equals 12.99

Answer 5

Sine Rule : sin 90 / 15 = sin 60 / x

Therefore, x = side opposite 60 deg
x = sin 60 / sin 90 * 15

Answer 6

This is about the 6 or 8th posting I have seen from you on this subject in about the past hour.
You need to stop having other people do your homework for you.

Answer 7

Thats easy, the perimeter of a triangle is always 180 degrees unless you are doing an equation like this. 6x+x2(3x).