A triangular swimming pool measures 45 ft on one side and 32

A triangular swimming pool measures 45 ft on one side and 32.6 ft on another side. The two sides form an angle that measures 41 degree How long is the third side? The length of the third side is ft. (Simplify your answer. Type an integer or a decimal. Round to the nearest tenth if needed.)

Solution

we can solve this question by using cosine law,We are using cosine law to answer this because the law of cosine is used for calculating third side of a triangle when we know the two sides and the angle between them that is angle between triangle.This law of cosine is very useful in solving the triangles.law of cosine states that

c²=a²+b²-2abcos(c) .Given a=45 ,b=32.6 and consider third side as x which we have to find, given angle=41degrees. substituting the values we get x²=(45)²+(32.6)²-2*45*32.6cos(41⁰) =2025+1062.76 -2934*0.7547

on simplyfying further we get x²=900.34 and x=30ft (near value).Hence the third side c=30 ft(nearly).