Question

If the area of an isosceles triangle is 60cm^2 and the length of each of its equal sides is 13cm, find its base.

Answer 1

Area of the isosceles triangle = 60 = (b^2 cos A)/2 = (13^2 cos A)/2 or

120 /13^2 = cos A, or

cos A = 120/169 = 0.710059171, or

<A - arc cos 0.710059171 = 44.76027011 deg and <A/2 = 22.38013505 deg

Base of the triangle = 2*13 sin 22.38013505 = 9.899494336 cm

Altitude of the triangle = 12.12183124 cm