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.
triangle with sides 14 (opposite? or adjacent? the triangle has side 14 at the top, side 7.5 on the left (from a), side 13 on the right), a is at the left vertex
a = °
question help: video ebook

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(b^{2}=a^{2}+c^{2}-2ac\cos B\). In \(\triangle ABC\) (assuming the sides opposite to angles \(A\), \(B\), \(C\) are \(a = 13\), \(b = 14\), \(c=7.5\)), for angle \(A\), we have \(a^{2}=b^{2}+c^{2}-2bc\cos A\). Rearranging for \(\cos A\): \(\cos A=\frac{b^{2}+c^{2}-a^{2}}{2bc}\).
Substitute \(a = 13\), \(b = 14\), \(c = 7.5\) into the formula:

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Step2: Find the angle \(A\)

Since \(A=\cos^{-1}(0.3964285714)\), using a calculator, \(A\approx66.7^{\circ}\)

Answer:

\(66.7\)