Posted by **jay** on Wednesday, October 7, 2009 at 7:46pm.

Help me I am lost? I do not even know where to start:

The shorter leg of a 30°–60°–90° triangle is 12. What are the lengths of the longer leg and the hypotenuse, to the nearest tenth?

- math -
**jim**, Wednesday, October 7, 2009 at 8:53pm
First, draw your triangle so you can see what you're doing. The short side, 12, will be opposite the small angle, 30.

We know that the sin of an angle = opposite over hypotenuse. The angle is 30, and we can look up sin(30)=0.5.

So opposite (which we know is 12) over hypotenuse = 1/2.

12/hypotenuse = 1/2

hypotenuse = 24.

Now we can get the final, adjacent, side in either of two ways:

1. Pythagoras: 12^2 + adjacent^2 = 24^2

or

2. use the definition of cos = adjacent over hypotenuse. We can look up cos(30) = sqrt(3)/2 or .8660. So:

adjacent/24 = .8660

and mutiply across from there.

- math -
**Reiny**, Wednesday, October 7, 2009 at 9:52pm
The sides of the 30-60-90 triangel are in the ratio of 1:√3:2

your triangle is 12:a:b

so 1/12 = √3/a

a = 12√3

and 1/12 = 2/b

b = 24

the other two sides are 12√3 and 24

## Answer This Question

## Related Questions

- math - The shorter leg of a 30°–60°–90° triangle is 10. What are the lengths of ...
- Geometry - The shorter leg of a 30 degree - 60 degree - 90 degree triangle is 10...
- math - did i do this right? The hypotenuse of a 30 ¨C 60-90 right triangle ...
- math - The hypotenuse of a right triangle is 1 cm more than twice the shorter ...
- math - the shorter leg of a right triangle is 9 inches shorter than the longer ...
- Quadratic Equations - The longer leg of a right triangle is 3 ft longer than ...
- Math - The length of the hypotenuse of a right triangle is 2m more than the ...
- Algebra - The hypotenuse of a right triangle is 13 inches long. The shorter leg ...
- math - The longer leg of a right triangle is 3 more than the shorter leg. The ...
- Math - A toy manufacturer needs a piece of plastic in the shape of a right ...

More Related Questions