Question

in the triangle abc if angle A =36 and angleB=64 name the longest and the shortest sides of a triangle

Answer 1

The longest side in triangle ABC is side b (opposite angle B) and the shortest side is side a (opposite angle A).

Step-by-step explanation:

In triangle ABC, if angle A = 36 and angle B = 64, we can determine the longest and shortest sides using the Law of Sines. This law states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

Let's call the longest side c, opposite to angle C, and the shortest side a, opposite to angle A.

Step 1: Find angle C: Angle C = 180 - Angle A - Angle B = 180 - 36 - 64 = 80 degrees.

Step 2: Apply the Law of Sines:
c/sin(C) = a/sin(A) = b/sin(B)

Step 3: Rearrange the equation:
a = c * sin(A) / sin(C) and b = c * sin(B) / sin(C)

Therefore, the longest side is side b (opposite to angle B) and the shortest side is side a (opposite to angle A).

Learn more about Triangle Sides