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°
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°.
To find the measure of angle G in triangle FGH, we can use the fact that the sum of the angles in a triangle is 180 degrees.
Given that angle F is 70 degrees, we can find angle H by subtracting angle F from 180 degrees:
m∠H = 180° - m∠F = 180° - 70° = 110°
Now, we have two angles of the triangle, angle F and angle H. To find angle G, we can subtract the sum of these two angles from 180 degrees:
m∠G = 180° - (m∠F + m∠H) = 180° - (70° + 110°) = 180° - 180° = 0°
However, this result doesn't seem plausible since a triangle with an angle of 0 degrees would not be a triangle. Therefore, it seems that there might be a mistake in the given information or question.
Please verify the information provided or double-check the angle measures and lengths of the sides of triangle FGH.
To find the measure of angle G, we can use the fact that the sum of the angles in a triangle is 180 degrees.
Step 1: Add up the given angle and the unknown angle: 70° + m∠G = 180°
Step 2: Subtract 70 from both sides of the equation: m∠G = 180° - 70°
Step 3: Calculate the value: m∠G = 110°
Step 4: Round the answer to the nearest tenth: m∠G ≈ 110°
Therefore, the measure of angle G is approximately 110 degrees.