Finding the height of a right triangle?

Question

I'm trying to find the height of a right triangle, which means the length of its vertical side. I have that the base angle is 90 degrees, the upper angle is 60 and the other angle is 30 degrees, and the length of the hypotenuse is 6. There must be some way to find the height of the triangle. So would like the answer and/or the formula to find it.

Thanks.

Answer 1

For a 30-60-90 triangle, the ratio between the 3 sides are:

Side adjacent to the 30 degree angle: sqrt(3)
Side adjacent to the 60 degree angle: 1
Hypotenuse: 2

Since the hypotenuse is 6, and the vertical side is adjacent to the 60 degree angle, we can form a ratio between the 2 sides.

2 / 1 = 6 / h

=> height = 3

Answer 2

3 times the square root of 3
it is a 30 60 90 triangle which means that the hypotenuse is half the length on the smaller length of the triangle
and that the longer length of the triangle is times by the square root of three

Answer 3

There are a few ways to do it, but the brute force method is to use the trigonometric way. As you have explained it, it sounds like the 30 degree angle is opposite the side you want.

So, sine = opposite/ hypotenuse

Let x be the length of the side opposite the 30 degree angle.

So, sin 30 = x/6
Sin 30=.5

So .5=x/6

Multiply both sides by 6, and you get:

x=3

Answer 4

in a 30-60-90 trinagle, the height is 1/2 of the hypotenuse. the answer to your question is 3

Answer 5

because the hypotenuse is 6 , one of the height is (6*sin 30=3),one is (6*cos 30=3√3). the square measure of this triangle is const ,so the product of multiplication between two vertical is equal to the product of multiplication between the hypotenuse and its height,is (6*sin 30 * 6*cos 30)/6=(3*3√3)/6=(3√3)/2
there are three height of this triangle
1. 3
2. 3√3
3. (3√3)/2

Answer 6

Using the bottom angle,
sinx = opposite / hypotenuse
sin30 = height / 6
height = 6sin30
height = 3.

Or using the top angle,
cosy = adjacent / hypotenuse
cos60 = height / 6
height = 6cos60
height = 3

Answer 7

30 60 90 degree triangle

sinθ = opposite / hypotenuse

sinθ = y / r

let

30° = angle A and opposite the vertex is the opposite side or y

sin30 = y / 6

6sin30 = 6(y/6)

6(0.5) = y

3 = y

The heigth is 3

- - - - - - - - s-

Answer 8

here, work it out:
http://www.webmath.com/geo_rtriangle.html
hope it helps

Answer 9

trigonometry