Question

A triangle has sides of length 11 m, 12 m, and 16 m.

Answer 1

We know that
 the law of cosines formulas established 
c²=a²+b²-2*a*b*cos C-----> cos C=[a²+b²-c²]/[2*a*b]
a=11 m
b=12 m
c=16 m
so
cos C=[11²+12²-16²]/[2*11*12]---> cos C=0.0341
C=arc cos (0.0341)-------> C=88.05°

see the attached figure

the answer is
the angle is 88°

Answer 2

Answer:

88 degrees.

Step-by-step explanation:

We have been given that a triangle has sides of length 11 m, 12 m, and 16 m. We are asked to find the measure of the angle opposite the side that is 16 m long.

To find the measure of angle opposite to 16 m side, we will use law of cosines.

$c^2=a^2+b^2-2ab\times cos(C)$, where a, b and c represent the side length of triangle. C represents the angle corresponding to side c.

Upon substituting our given values in above formula we will get,

$16^2=11^2+12^2-2\times 11\times 12\times cos(C)$

$256=121+144-264\times cos(C)$

$256=265-264\times cos(C)$

$256-265=265-265-264\times cos(C)$

$-9=-264\times cos(C)$

$\frac{-9}{-264}=\frac{-264\times cos(C)}{-264}$

$\frac{-9}{-264}=cos(C)$

Now we will use inverse cos formula to solve for C.

$cos^{-1}(\frac{-9}{-264})=C$

$88.046356247078^{\circ}=C$

Upon rounding our answer to nearest degree we will get,

$C=88^{\circ}$

Therefore, the measure of angle opposite to the 16 m long side is 88 degrees.