Question

question
in δfgh, f = 600 cm, m∠f = 32°, and m∠g = 12°. find the length of h, to the nearest 10th of a centimeter.
answer attempt 3 out of 3
h =
cm
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Explanation:

Step1: Find angle at H

In a triangle, the sum of angles is \(180^\circ\). So \(m\angle H=180^\circ - 32^\circ - 12^\circ=136^\circ\).

Step2: Apply Law of Sines

Law of Sines: \(\frac{h}{\sin G}=\frac{f}{\sin H}\). We know \(f = 600\) cm, \(m\angle G = 12^\circ\), \(m\angle H=136^\circ\). So \(\frac{h}{\sin12^\circ}=\frac{600}{\sin136^\circ}\).

Step3: Solve for h

\(h=\frac{600\times\sin12^\circ}{\sin136^\circ}\). Calculate \(\sin12^\circ\approx0.2079\), \(\sin136^\circ=\sin(180^\circ - 44^\circ)=\sin44^\circ\approx0.6947\). Then \(h=\frac{600\times0.2079}{0.6947}\approx\frac{124.74}{0.6947}\approx179.6\) (rounded to nearest tenth).

Answer:

\(179.6\)