Question

I will give you 100 points

Answer 1

Answer:

m∠C = 110.9° (1 dp)

Step-by-step 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:

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

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

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

$\implies \sf \cos C=\dfrac{225-170}{-154}$

$\implies \sf \cos C=-\dfrac{5}{14}$

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

$\implies \sf C=110.9248324...^{\circ}$

Therefore, m∠C = 110.9° (1 dp)

Answer 2

Answer:

see photo for detailed analysis