Final answer:
To find the length of h in ΔFGH, we can use the Law of Sines to set up a proportion. Evaluating the trigonometric functions gives us the length of h to be approximately 163.6 cm.
Step-by-step explanation:
To find the length of h in the triangle ΔFGH, we can use the Law of Sines. The Law of Sines states that in any triangle, the ratio of the length of a side to the sin of its opposite angle is constant. In this case, we have the lengths of side f and the measures of angles F and G, so we can set up the following proportion:
f/sin(F) = h/sin(G)
Substituting the known values, we have:
600/sin(32°) = h/sin(12°)
Solving for h, we get:
h = (600 * sin(12°)) / sin(32°)
Using a calculator to evaluate the trigonometric functions, we find that h ≈ 163.6 cm. Therefore, the length of h, to the nearest 10th of a centimeter, is 163.6 cm.