Question

in triangle abc, ab = 90 in., bc = 80 in., and angle b measures 50°. what is the approximate perimeter of the triangle?
242.4 in.
265.3 in.
308.3 in.
324.1 in.

Explanation:

Step1: Use the Law of Cosines to find \(AC\)

The Law of Cosines formula is \(AC^{2}=AB^{2}+BC^{2}-2(AB)(BC)\cos B\).
Substitute \(AB = 90\), \(BC = 80\), and \(B = 50^{\circ}\) (\(\cos50^{\circ}\approx0.6428\)):

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Then \(AC=\sqrt{5242.72}\approx72.4\)

Step2: Calculate the perimeter \(P\)

The perimeter \(P=AB + BC+AC\).
Substitute \(AB = 90\), \(BC = 80\), and \(AC\approx72.4\):
\(P=90 + 80+72.4=242.4\)

Answer:

242.4 in.