Question

Use the triangle below to find the measure of angle G.

Answer 1

59.3° (nearest tenth)

Explanation:

Cosine Rule (for finding angles)

`\boxed{\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

From inspection of the given triangle:

• C = angle G
• a = side GI = 6
• b = side GH = 15
• c = side HI = 13

Substitute the values into the formula and solve for G:

`\implies \sf \cos(G)=(6^2+15^2-13^2)/(2(6)(15))`

`\implies \sf \cos(G)=(36+225-169)/(180)`

`\implies \sf \cos(G)=(92)/(180)`

`\implies \sf G=\cos^(-1) \left((92)/(180)\right)`

`\implies \sf G=59.26213133...^(\circ)`

Therefore, the measure of angle G is 59.3° (nearest tenth).