Question

In a triangle ABC .side AB is 80 and perimeter is 170 and angle ABC is 60 find the smallest 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

Answer 2

Answer:

The measure of the smallest side of the given triangle will be equal to 17cm.

Step-by-step explanation:

Let the remaining two sides of the triangle be x and y respectively.

We are given that AB=80

Perimeter = 170.

We know that perimeter is equal to sum of all sides.

Therefore,

x+y+80 = 170 (Given)

x + y  = 90  ---- (1)

Using cosine rule,

cos β = (a² + c² - b²)/(2 * a * c)

cos 60 = ( x² + 80² - y² ) /  ( 2 * x * 80  )

1/2 = ( x² + 80² - y² ) /  ( 160 x  )  --- (2)

When Solving (1) and (2) we get,

x = 17, y = 73

Therefore the smallest side of the triangle = 17 cm