Question

In ΔABC, if the length of sides a, b, and c are 3.5 centimeters, 5.5 centimeters, and 6 centimeters respectively, what is m∠C to two decimal places?

Answer 1

Answer: C 80.28

Explanation:

Answer 2

We start by sketching the triangle ABC as shown below. We label the side with the small letters a,b, and c on the opposite of the angle A, B, and C

The angle m<C is labeled x

To work out the size of x, we use the cosine rule

`c^(2)= a^(2)+ b^(2)-2ab(cos(x))`

`6^(2)= 3.5^(2)+ 5.5^(2)-(2)(3.5)(5.5)(cos(x))`

`36=12.25+30.25-(38.5cos(x))`

`36=42.5-38.5cos(x)`

`36-42.5=-38.5cos(x)`

`-6.5=-38.5cos(x)`

`cos(x)= (6.5)/(38.5)`

`image`5} )}[/tex] to one decimal place