Question

quiz 8: solve right, scalene, and obtuse triangles
6 points possible answered: 5/6
question 6
find the measure of ∠a. round to the nearest tenth of a degree.
20.3
9.9 18.8
a = °
question help: video ebook

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(a^{2}=b^{2}+c^{2}-2bc\cos A\). Let \(a = 20.3\), \(b = 18.8\), \(c = 9.9\). Then \(\cos A=\frac{b^{2}+c^{2}-a^{2}}{2bc}\).
Substitute the values: \(\cos A=\frac{18.8^{2}+9.9^{2}-20.3^{2}}{2\times18.8\times9.9}\).
First calculate the squares: \(18.8^{2}=353.44\), \(9.9^{2}=98.01\), \(20.3^{2}=412.09\).
Then \(b^{2}+c^{2}-a^{2}=353.44 + 98.01-412.09=39.36\).
And \(2bc=2\times18.8\times9.9 = 372.24\).
So \(\cos A=\frac{39.36}{372.24}\approx0.1057\).

Step2: Find the angle \(A\)

Since \(A=\cos^{-1}(0.1057)\).
Using a calculator, \(A\approx83.9^{\circ}\).

Answer:

\(83.9\)