Question

Find the missing parts of the triangle. (Find angles to the nearest hundredth of a degree.)

a = 7.5

b = 13.3

c = 16.0

Answer 1

`A \approx 27.75^(\circ)`,
`B \approx 55.67^(\circ)`,
`C \approx 96.60^(\circ)`

Explanation:

The first two angle can be determined by the Law of the Cosine:

`\cos A = (7.5^(2)-13.3^(2)-16^(2))/(-2\cdot (13.3)\cdot (16))`

`\cos A = 0.885`

`A = \cos^(-1) 0.885`

`A \approx 27.75^(\circ)`

`\cos B =(13.3^(2)-7.5^(2)-16^(2))/(-2\cdot (7.5)\cdot (16))`

`\cos B = 0.564`

`B = \cos^(-1) 0.564`

`B \approx 55.67^(\circ)`

`\cos C = (16^(2)-7.5^(2)-13.3^(2))/(-2\cdot (7.5)\cdot (13.3))`

`\cos C = -0.115`

`C = \cos^(-1) (-0.115)`

`C \approx 96.60^(\circ)`

The sum of internal angles of a triangle must be equal to 180°. Then:

`A + B + C = 27.75^(\circ) + 55.67^(\circ) + 96.60^(\circ)`

`A + B + C = 180.02^(\circ)`

Which satisfies the condition described.