Question

Chris is working on a stained-glass project and needs to form a triangle with sides of 8, 12, and 15 inches out of lead cane to enclose the glass. To the nearest tenth of a degree, what is the largest angle he needs to create using the lead caning?

Answer 1

The largest angle needed is
`95.1^(o)`.

Explanation:

To determine the larges angle as required, let us apply the cosine rule.

`c^(2)` =
`a^(2)` +
`b^(2)` - 2ab Cos C

Since in triangles, the longest side is opposite to the largest angle, then;

`15^(2)` =
`8^(2)` +
`12^(2)` - 2(8 x 12) Cos θ

225 = 64 + 144 - 192 Cos θ

225 = 208 - 192 Cos θ

192 Cos θ = 208 -225

192 Cos θ = -17

Cos θ =
`(-17)/(192)`

Cos θ = -0.08854

θ =
`Cos^(-1)` -0.08854

= 95.07962

θ =
`95.1^(o)`

The largest angle needed is
`95.1^(o)`.