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

Answer:

The largest angle needed is $95.1^{o}$.

Step-by-step 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 = $\frac{-17}{192}$

Cos θ = -0.08854

θ = $Cos^{-1}$ -0.08854

  = 95.07962

θ = $95.1^{o}$

The largest angle needed is $95.1^{o}$.