In an isosceles triangle, the height drawn to the base is 7 cm, and its lateral side is 14 cm. Find the largest angle of the triangle.
| February 6, 2021 | education
1. Vertices of the triangle – A, B, C. AB = BC = 14 centimeters. ВН – height drawn to
base.
2. In a right-angled triangle ABН, the height of the ВН is a leg, and the side of the triangle
AB – hypotenuse. The length of the hypotenuse is 2 times the length of the leg (14: 7 = 2).
Therefore, ∠ВАН (∠А) = 30 °.
3. According to the properties of an isosceles triangle, the angles at its base are equal.
Therefore, ∠ A = ∠C = 30 °.
4. We calculate the value of ∠В:
∠В = 180 ° – ∠А – ∠С = 180 ° – 30 ° – 30 ° = 120 °.
∠В = 120 ° – the largest of all the angles of the triangle.
Answer: the largest angle of the triangle is ∠B = 120 °.
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