Answer :
∠F, to the nearest degree, is approximately 38 degrees.
To find ∠F in triangle FGH, we can use the fact that the sum of the angles in a triangle is always 180 degrees. Let's calculate ∠F step by step:
1. Find ∠H by subtracting ∠G from 180 degrees:
∠H = 180° - ∠G = 180° - 149° = 31°
2. Use the Law of Sines to find the ratio between the lengths of sides f and h:
sin(∠F) / f = sin(∠H) / h
3. Substitute the values we know into the equation:
sin(∠F) / 150 = sin(31°) / 210
4. Rearrange the equation to solve for sin(∠F):
sin(∠F) = (150 / 210) * sin(31°)
5. Calculate the value of sin(∠F) using a calculator:
sin(∠F) ≈ 0.614
6. Find the inverse sine (sin⁻¹) of 0.614 to find the measure of ∠F:
∠F ≈ sin⁻¹(0.614) ≈ 37.6°
Therefore, ∠F, to the nearest degree, is approximately 38 degrees.
