An isosceles triangle has a base with length 15 inches and two congruent sides with lengths of 15 inches each. find the height of the triangle. (round your answer to the nearest tenth of an inch.)

An isosceles triangle is a special triangle having at least 2 equal sides equal. But in this case, since all sides are equal having a length of 15 inches, this is actually an equilateral triangle. 

When you create a perpendicular bisector from the top vertex to the midpoint of the base, you get a right triangle with the hypotenuse equal to 15 inches, a base equal to half of 15 because it was bisected, and the height. Therefore, we use the pythagorean theorem. The solution would be

h = √(15)^2 +(15/2)^
h = 13.0 meters

30 degrees

Angles ACB and CAB are both 75 degrees due to the fact that they are 90 degree angles subtracting the 15 degrees. Then add the two together and subtract from 180.