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:
[tex]\sf c^2=a^2+b^2-2ab \cos C[/tex]
(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:
[tex]\implies \sf c^2=a^2+b^2-2ab \cos C[/tex]
[tex]\implies \sf 15^2=11^2+7^2-2(11)(7) \cos C[/tex]
[tex]\implies \sf 225=170-154 \cos C[/tex]
[tex]\implies \sf \cos C=\dfrac{225-170}{-154}[/tex]
[tex]\implies \sf \cos C=-\dfrac{5}{14}[/tex]
[tex]\implies \sf C=\cos ^{-1}\left(-\dfrac{5}{14}\right)[/tex]
[tex]\implies \sf C=110.9248324...^{\circ}[/tex]
Therefore, m∠C = 110.9° (1 dp)
