Answer:
∠S = 36.4
Step-by-step explanation:
Given:
Where:
- s = 39 in
- t = 18 in
- u = 52 in
To find the value of ∠S we can use the Cosine Rule
\(s^2 = t^2 + u^2 - 2tu \times \cos(S)\)
Making cos(S) the subject of the formula
\(2tu \times \cos(S) = t^2 + u^2 - s^2\)
\(cos(S) = \frac{t^2 + u^2 - s^2}{2tu}\)
\(cos(S) = \frac{18 in^2 + 52 in^2 - 39 in^2}{2 \times 18 in \times 52 in}\)
\(\cos(S) = \frac{324in^2 + 2704 in^2 - 1521 in^2}{1872 in^2}\)
\(\cos(S) = \frac{1507 in^2}{1872 in^2}\)
\(\cos(S) = 0.8050\)
\(\angle S = \cos^{-1}(0.8050)\)
\(\angle S \approx 36.4\)
