In an isosceles triangle ABC with base AC, the side AB is 15, cosB = -0.8, AH-height, Find the line segment CH

Pay attention to the fact that the cosine is negative, which means the angle B is obtuse and the height AH will fall on the continuation of the BC side. The segment BH then consists of two parts – the side BC and the continuation of this side Н.
CH = BC + BH.
ABC – isosceles, AB = BC = 15 cm.
From the right-angled triangle ABН we find BН = A * cosABН. Note that angle ABH adjacent to angle B, then
сosАВН = -cosВ = 0.8.
BH = 15 * 0.8 = 12 (cm).
CH = 12 + 15 = 27 (cm).