Find the area of an isosceles triangle with a side side of 10 cm if the angles of this triangle are 5: 2: 5

1. Vertices of the triangle A, B, C. AB = BC = 10 centimeters.

2. We take for x the number of degrees per part.

3. By the condition of the problem, the given triangle is isosceles. Therefore, ∠A = ∠C = 5x. ∠B = 2x.

4. Considering that the sum of the interior angles of the triangle is 180 °, we compose the equation:

2x + 5x + 5x = 180 °.

12x = 180 °.

x = 15 °.

∠А = ∠С = 5 x 15 = 75 °.

∠B = 2 x 15 = 30 °.

5. Calculate the area (S) of a given triangle:

S = AB x BC / 2 x sine ∠B.

Sine ∠B = sine 30 ° = 1/2.

S = 10 x 10/4 = 25 centimeters².

Answer: The area of a given triangle is 25 centimeters².