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yanalaym [24]
3 years ago
6

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

?

Mathematics
1 answer:
Crank3 years ago
7 0

Answer:

Length of the side opposite to angle 116^{\circ} is 31.49

Step-by-step 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}}=\sqrt{991.59}

a=31.49

Therefore length of third side is 31.49

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