Question

what is the measure of ∠c to the nearest whole degree? 70° 77° 80° 85° law of cosines: ( a^2 = b^2 + c^2 - 2bccos(a) ) (triangle with right angle at b, ab = 8.77, bc = 2, ac = 9)

Explanation:

Step1: Use the sine function

In a right - triangle, \(\sin C=\frac{AB}{AC}\). Given \(AB = 8.77\) and \(AC=9\).
So, \(\sin C=\frac{8.77}{9}\).

Step2: Calculate the value of \(\sin C\)

\(\frac{8.77}{9}\approx0.9744\).

Step3: Find the angle \(C\)

We know that if \(\sin C = x\), then \(C=\sin^{- 1}(x)\). So \(C=\sin^{-1}(0.9744)\).
Using a calculator, \(C\approx77^{\circ}\).

Answer:

\(77^{\circ}\)