If the degrees of a triangle are 90º, 30º, and 60º what are its sides? one side is 15.

Question

It looks like this, |\ the straight side is 15. 30º is opposite to measure 15.

Answer 1

In a 30-60-90 right triangle, the short leg, the leg opposite the 30º angle, is always one-half the hypotenuse, and the long leg is always the short leg times √3.

If 15 is opposite the 30º angle, then 15 is the short leg and the long leg is 15√3. The hypotenuse is therefore twice the short leg, or 2*15=30.

check: 30^2=15^2+(15√3)^2, 900=225+675=900

 

If 15 is not opposite the 30º angle, then 15 is the long leg and the long leg is the short leg times √3. Call the short leg "x". Therefore 15=√3x, x=15/√3=15√3/3=5√3. The short leg is 5√3, the long leg is 15, and the hypotenuse is twice the short leg which means the hypotenuse is 2*5√3=10√3.

check: (10√3)^2=(5√3)^2+15^2, 300=75+225=300