Question

A triangle has two sides measuring 16 and 21. The included angle is 116°. What is the length of the side opposite the 116° angle?

Answer 1

Length of the side opposite to angle
`116^(\circ)` is 31.49

Explanation:

Included angle can be defined as the angle in between two sides of the triangle.

So angle
`116^(\circ)` is in between sides 16 and 21.

Refer to the attachment for triangle diagram.

To find the length of opposite side, use cosine rule as follows

`a^(2)=b^(2)+c^(2)-2\:b\:c\cos\left(A\right)`

From the diagram,
`b = 21,c = 16,\angle A=116^(\circ)`

Substituting the values in the formula,

`a^(2)=\left(21\right)^(2)+\left(16\right)^(2)-2\left(21\right)\left(16\right)\cos\left(116\right)`

Simplifying,

`a^(2)=441+256-225792\left(-0.44\right)`

`a^(2)=991.59`

Taking square root on both sides,

`\sqrt{a^(2)}=√(991.59)`

`a=31.49`

Therefore length of third side is 31.49