Question

kyung is building a triangular pool in his backyard. he knows that side f is 12 m and that both angles g and f are 40°, which means that angle d is 100°. what is the length of side d? round the answer to the nearest tenth.

Explanation:

Step1: Apply the Law of Sines

The Law of Sines states that \(\frac{d}{\sin D}=\frac{f}{\sin F}\).

Step2: Substitute the known values

We know \(f = 12\) m, \(D=100^{\circ}\), \(F = 40^{\circ}\). So \(d=\frac{f\times\sin D}{\sin F}\).
Substituting the values: \(d=\frac{12\times\sin(100^{\circ})}{\sin(40^{\circ})}\).
Since \(\sin(100^{\circ})\approx0.9848\) and \(\sin(40^{\circ})\approx0.6428\).
Then \(d=\frac{12\times0.9848}{0.6428}\).

Step3: Calculate the value of \(d\)

\(12\times0.9848 = 11.8176\).
\(d=\frac{11.8176}{0.6428}\approx18.4\).

Answer:

\(18.4\) m