Question

I will give you 100 points

Answer 1

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:

• a = BC = 11cm
• b = AC = 7 cm
• c = AB = 15 cm

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)

Answer 2

see photo for detailed analysis