In an isosceles trapezoid, we know the height BH = 5, the larger base AD = 15

In an isosceles trapezoid, we know the height BH = 5, the larger base AD = 15, and the angle at the base A = 45. Find the smaller base.

Since VN is the height of the trapezoid, then the triangle ABН is rectangular, and since the angle is A = 45, then AH = BH = 5 cm.

Let’s build the height of the CК of the trapezium AВСD. In an isosceles trapezoid, the segments cut off by heights on the larger base are equal. Then DK = AH = 5 cm.

Then НK = AD – AН – DK = 15 – 5 – 5 = 5 cm.

Quadrangle ВСKН is a rectangle, then ВС = НK = 5 cm.

Answer: The length of the smaller base is 5 cm.