To find m∠G, we can use the law of sines which states that in any triangle ABC,
a/sin(A) = b/sin(B) = c/sin(C)
where a, b, c are the lengths of the sides opposite angles A, B, and C respectively. Rearranging this formula, we get:
sin(A)/a = sin(B)/b = sin(C)/c
In ΔFGH, we have:
sin(F)/FH = sin(G)/FG
sin(70°)/7 = sin(G)/12
sin(G) = 12 sin(70°)/7
Using a calculator, we can find:
sin(G) ≈ 0.989
Now, we need to find the angle whose sine is 0.989. We can use the arcsine function or inverse sine function on our calculator to find this angle. The answer is:
m∠G ≈ 78°
Therefore, the correct answer is option C) 78°.
In ΔFGH, FH = 7ft, FG = 12ft, and m∠F = 70°. Find m∠G. Round your answer to nearest tenth.
17.3°
11.6°
78°
34.4°
1 answer
1 answer