Question

Side ab of a triangle abc is 80 cm. If the perimeter is 170 and angle abc is 60. Find the shortest side

Answer 1

Answer:

17 cm

Step-by-step explanation:

Let the remaining side be a and b respectively.

Since the perimeter = 170 cm and one of the side is 80, then

a + b = 90  ---- (1)

Based on cosine rule,

cos 60 = ( a² + 80² - b² ) /  ( 2 x a x 80  )

1/2 = ( a² + 80² - b² ) /  ( 160 a  )  --- (2)

Solving (1) and (2) we get,

a = 17, b = 73

So the smallest side = 17 cm