College

In ΔFGH, [tex]h = 210 \, \text{cm}[/tex], [tex]f = 150 \, \text{cm}[/tex], and [tex]\angle G = 149^\circ[/tex]. Find [tex]\angle F[/tex], to the nearest degree.

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.