Question

In a triangle, suppose we know that side b=3 feet, side c=2 feet, and that angle A=140o. According to the Law of Cosines, the length of side a is approximately?

Answer 1

The length of third side of triangle is 4.195 feet.

Explanation:

In a triangle as shown in the figure the law of cosines states that

`a^(2)=c^(2)+b^(2)-2bccos(A)`

Since it is given that

b = 3 feet

c = 2 feet

A =
`140^(o)`

Using these values in the above equation we get

`a^(2)=2^(2)+3^(2)-2* 3* 2cos(140)\\\\\therefore a^(2)=17.596\\\\a=4.195feet`