Question

The altitudes of a triangle are 12 15 and 20. the largest angle in the triangle is

Answer 1

Answer:

largest angle in the triangle is 90°

Step-by-step explanation:

The altitudes of a triangle are 12 15 and 20. the largest angle in the triangle is

Area of triangle = (1/2) * base * altitude

(1/2) * Side1 * 12 = (1/2) * Side2* 15 = (1/2) * Side3 * 20  = 30K

=> side 1 = 5K

Side 2 = 4K

Side 3 = 3K

Angle opposite to largest side = Largest angle

(5K)² = (3K)² + (4K)² - 2 * 3K*4KCosα

=> 25K² = 9K² + 16K² - 24K²Cosα

=> 24K²Cosα = 0

=> Cosα  = 0

=> α = 90°

largest angle in the triangle is 90°