Question

In a triangle ABC, if the measure of sides opposite to their corresponding angles are 13,14,15 then what are the measures of the angles?

Answer 1

To find the measures of the angles in triangle ABC with side lengths 13, 14, and 15, we can use the Law of Cosines.

Step-by-step explanation:

Given the lengths of the sides of triangle ABC are 13, 14, and 15, we can use the Law of Cosines to find the measures of the angles.

The Law of Cosines states that in a triangle with sides a, b, and c, and angle C opposite side c, we have: c^2 = a^2 + b^2 - 2ab*cos(C).

Using this formula, we can find the measures of the angles:

Angle A = acos((b^2 + c^2 - a^2)/(2*b*c))

Angle B = acos((a^2 + c^2 - b^2)/(2*a*c))

Angle C = acos((a^2 + b^2 - c^2)/(2*a*b))

Plugging in the values, we get:

Angle A = acos((14^2 + 15^2 - 13^2)/(2*14*15))

Angle B = acos((13^2 + 15^2 - 14^2)/(2*13*15))

Angle C = acos((13^2 + 14^2 - 15^2)/(2*13*14))

Solving these equations will give us the measures of the angles.