The length of the shorter leg of a 30°-60°-90° triangle is 5 cm. What is the length of the longer leg? What is the length of the hypotenuse?

Answer 1

There multiple ways to solve this problem. You have all the angles and you have one of the sides.

The angles are 30 degrees, 60 degrees, and 90 degrees. Shorter side is 5 cm.

Use the basic trig functions to solve the problem. A trig function is the ratio of one side to another. In this case of the sine function is the opposite divided by the hypotenuse.

In any triangle the size of the opposite side is related to the size of the angle. - the longer the side the bigger the angle. The text said the shorter side was 5 cm. Therefore, that side is opposite the 30 degree angle. The sine of 30 degrees is 1/2.

Set up a direct proportion as follows:

1 5

---- = ---- (cross- multiply ) hyp = 10 cm

2 hyp

To find the remaining side - you have several choices. You could use a trig function or the pythagorian theorem.

First I will use the tan functiom. the tan of 30 degrees is 1/sqrt(3). use the same process.

1 5

---- = ---- otherside = 5(sqrt(3)) about 8.66

sqrt(3) otherside

using the theorem b = sqrt( c^2 - b^2)

b = sqrt(10^2 -5^2) = sqrt(100 - 25) = sqrt(75) = about 8.66

30 degrees, 60 degrees, and 45 degrees are a set of very special and commonly used angles.

If you have not already memorized the trig function values for these angles, it would be a good idea to do so.

Answer 2

Hi Jake

There is a special relationship between the sides of a 30° 60° 90° right triangle. If the leg opposite the smallest angle 30°, the shortest leg is 1, the leg opposite the 60° is 1*√3, and the leg opposite the largest angle 90° is 2*1.

If you plug in 5 for one you will obtain the other sides

30° side opposite is the shortest leg = 5

60° side opposite is the longer leg = 5√3

90° side opposite is the longest leg = 10

I hope you find this useful. You can look up the relationship between the sides of this and other Right triangles online.

Answer 3

a 30-60-90 triangle has sides in a ratio of 1:3^1/2:2 for short side: longer side: hypotenuse

If the shortest side is 5 cm, the longer side is square root of 3 times 5 cm. and the hypotenuse is 5x2 = 10 cm.