Answer:
59.3° (nearest tenth)
Step-by-step explanation:
Cosine Rule (for finding angles)
[tex]\boxed{\sf \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}}[/tex]
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:
[tex]\implies \sf \cos(G)=\dfrac{6^2+15^2-13^2}{2(6)(15)}[/tex]
[tex]\implies \sf \cos(G)=\dfrac{36+225-169}{180}[/tex]
[tex]\implies \sf \cos(G)=\dfrac{92}{180}[/tex]
[tex]\implies \sf G=\cos^{-1} \left(\dfrac{92}{180}\right)[/tex]
[tex]\implies \sf G=59.26213133...^{\circ}[/tex]
Therefore, the measure of angle G is 59.3° (nearest tenth).
