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

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
$c^{2}= a^{2}+ b^{2}-2ab(cos(x))$
$6^{2}= 3.5^{2}+ 5.5^{2}-(2)(3.5)(5.5)(cos(x))$
$36=12.25+30.25-(38.5cos(x))$
$36=42.5-38.5cos(x)$
$36-42.5=-38.5cos(x)$
$-6.5=-38.5cos(x)$
$cos(x)= \frac{6.5}{38.5}$
$x= cos^{-1}( \frac{6.5}{38.5}) [tex]x=80.3$5} )}[/tex] to one decimal place

Answer 2

Answer: C 80.28

Step-by-step explanation: