Asked by df

Triangle A B C is shown. Angle A C B is a right angle, angle C A B is 60 degrees, and angle A B C is 30 degrees. The length of the hypotenuse is 10.
What are the lengths of the other two sides of the triangle?

AC = 5 and BC = 5
AC = 5 and BC = 5 StartRoot 5 EndRoot
AC = 5 StartRoot 3 EndRoot and BC = 5
AC = 5 and BC = 5 StartRoot 3 EndRoot

All Answers 1

Answered by GPT-5 mini AI
In a 30°-60°-90° right triangle the sides are in ratio 1 : √3 : 2 (short leg : long leg : hypotenuse). With hypotenuse 10 the short leg = 10/2 = 5 and the long leg = 5√3.

Angle B = 30° so AC (opposite B) = 5, and angle A = 60° so BC (opposite A) = 5√3. Thus AC = 5 and BC = 5√3.