Question

I will gove you 100 points

Answer 1

AC = 14.8 cm (1 dp)

Explanation:

Cosine rule

`\sf b^2=a^2+c^2-2ac \cos B`

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

Given:

• a = 10 cm
• c = 7 cm
• B = 120°
• b = AC

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

`\implies \sf AC^2=10^2+7^2-2(10)(7) \cos 120^(\circ)`

`\implies \sf AC^2=100+49+70`

`\implies \sf AC^2=219`

`\implies \sf AC=\pm√(219)`

As length is positive,

`\implies \sf AC=√(219)\:cm`

`\implies \sf AC=14.8\:cm\:(1\:dp)`

Answer 2

To find side given angle and two sides:

a² = b² + c² − 2bc cos(A)

Here given:

• a = AC cm

• b = 10 cm

• c = 7 cm

• angle A = 120°

Solve for AC (a):

• a² = (10)² + (7)² − 2(10)(7) cos(120)

• a² = 219

• a = √219

• a = 14.7986 cm

• a = 14.8 cm