Question

given the triangle
28
a
16
25
, find the measure of angle a using the law of cosines.
picture is not drawn to scale
a =
degrees
give your answer accurate to at least one decimal place
question help:
video

Explanation:

Step1: Recall the Law of Cosines formula

The Law of Cosines formula is \(a^{2}=b^{2}+c^{2}-2bc\cos A\). In a triangle with sides \(a = 16\), \(b = 25\), \(c = 28\), we can rewrite the formula to solve for \(\cos A\): \(\cos A=\frac{b^{2}+c^{2}-a^{2}}{2bc}\).

Step2: Substitute the values into the formula

Substitute \(a = 16\), \(b = 25\), \(c = 28\) into \(\cos A=\frac{b^{2}+c^{2}-a^{2}}{2bc}\).

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Step3: Find the angle \(A\)

Since \(A=\cos^{-1}(0.8236)\), using a calculator, \(A\approx34.6^{\circ}\)

Answer:

\(34.6\)