I will give you 100 points

Question

asked May 20, 2023 195k views

2 Answers

Geschema · Answer 1 · 2023-05-23T05:26:50+0000

Answer:

m∠C = 110.9° (1 dp)

Explanation:

The largest angle in a triangle is opposite the longest side.

Therefore, from inspection of the diagram, angle C is the largest angle since length AB is the longest side length.

To find angle C, use the cosine rule:

$\sf c^2=a^2+b^2-2ab \cos C$

(where a, b and c are the sides, and C is the angle opposite side c)

Given:

Substituting the given values into the formula and solving for C:

$\implies \sf c^2=a^2+b^2-2ab \cos C$

$\implies \sf 15^2=11^2+7^2-2(11)(7) \cos C$

$\implies \sf 225=170-154 \cos C$

$\implies \sf \cos C=(225-170)/(-154)$

$\implies \sf \cos C=-(5)/(14)$

$\implies \sf C=\cos ^(-1)\left(-(5)/(14)\right)$

$\implies \sf C=110.9248324...^(\circ)$

Therefore, m∠C = 110.9° (1 dp)