In an isosceles triangle, DEF DE = EF. The height DH forms an angle of 15 ° with the base DF. Find DE if DH = 4 cm.

Having drawn the height in the triangle DEF, we get the newly formed triangle DHF.

Δ DHF – rectangular, <DHF = 90 (since DH ┴ EF), <HDF = 15 (by condition), <HFD = 180 – (90 + 15) = 75 (The sum of the angles of the triangle is 180 degrees).

<EDF = 75 because in an isosceles triangle, the base angles are <EDF = <EFD.

<DEF = 180 – (75 + 75) = 30.

Δ DEH – right-angled, and in a right-angled triangle, the leg opposite to an angle of 30 degrees is equal to half the hypotenuse, DH = 1/2 * DE.

DE = 2 * DH;

DE = 2 * 4 = 8 (cm).

Answer. 8 cm.