How to find the corners of an isosceles triangle with a height of 7.6 cm; and the side of the triangle is 15.2 cm.

An isosceles triangle is a triangle in which the sides are equal:

AB = BC;

Its height is also the bisector and median, thus dividing it into two equal right-angled triangles.

Consider the triangle ΔАВН. To calculate the value of the angle ∠A, we apply the theorem of sines:

sin A = BH / AB;

sin A = 7.6 / 15.2 = 1/2;

1/2 = sin 30º.

Since in an isosceles triangle the angles at the base are equal, then:

∠А = ∠С = 30º.

Since the sum of all the angles of the triangle is 180º, then:

∠В = 180º – ∠А – ∠С;

∠В = 180º – 30º – 30º = 120º.

Answer: angles ∠А and ∠С are equal to 30º, angle ∠В is equal to 120º.