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?
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.
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
To find the lengths of the longer leg and the hypotenuse of a 30°–60°–90° triangle, we can use the ratios between the sides of this special triangle.
In a 30°–60°–90° triangle, the ratio between the lengths of the sides is as follows:
- The length of the shorter leg is x.
- The length of the longer leg is x√3.
- The length of the hypotenuse is 2x.
Given that the length of the shorter leg is 12, we know that x = 12.
To find the length of the longer leg, we can use the formula: longer leg = x√3.
Plugging in the value of x, we get: longer leg = 12√3 ≈ 20.8 (rounded to the nearest tenth).
To find the length of the hypotenuse, we can use the formula: hypotenuse = 2x.
Plugging in the value of x, we get: hypotenuse = 2 * 12 = 24.
Therefore, the length of the longer leg is approximately 20.8 and the length of the hypotenuse is 24.