Question

What is angle Data please help

Answer 1

C. 74°

Explanation:

Cosine Rule (for finding angles)

`\sf \cos(C)=(a^2+b^2-c^2)/(2ab)`

where:

• C = angle
• a and b = sides adjacent the angle
• c = side opposite the angle

Given:

• C =
  `\theta`
• a = 5
• b = 11
• c =
  `\sf √(115)`

Substitute these values into the formula:

`\implies \sf \cos(\theta)=(5^2+11^2-(√(115))^2)/(2(5)(11))`

`\implies \sf \cos(\theta)=(25+121-115)/(110)`

`\implies \sf \cos(\theta)=(31)/(110)`

`\implies \sf \theta=\cos^(-1)\left((31)/(110)\right)`

`\implies \sf \theta=74^(\circ) \quad (nearest\:degree)`