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In ΔSTU, s = 39 inches, t = 18 inches and u=52 inches. Find the measure of ∠S to the nearest 10th of a degree.

Sagot :

chibabykalu16

Answer:

∠S = 36.4

Step-by-step explanation:

Given:

  • ΔSTU

Where:

  • s = 39 in
  • t = 18 in
  • u = 52 in

To find the value of ∠S we can use the Cosine Rule

[tex]s^2 = t^2 + u^2 - 2tu \times \cos(S)[/tex]

Making cos(S) the subject of the formula

[tex]2tu \times \cos(S) = t^2 + u^2 - s^2[/tex]

[tex]cos(S) = \frac{t^2 + u^2 - s^2}{2tu}[/tex]

[tex]cos(S) = \frac{18 in^2 + 52 in^2 - 39 in^2}{2 \times 18 in \times 52 in}[/tex]

[tex]\cos(S) = \frac{324in^2 + 2704 in^2 - 1521 in^2}{1872 in^2}[/tex]

[tex]\cos(S) = \frac{1507 in^2}{1872 in^2}[/tex]

[tex]\cos(S) = 0.8050[/tex]

[tex]\angle S = \cos^{-1}(0.8050)[/tex]

[tex]\angle S \approx 36.4[/tex]

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