Question

what is the measure of ∠c in the triangle above? (degrees?) options: 90°, 77°, 70°, 65°. triangle has right angle at b, bc = 2, ab = 8.77, ac = 9 (approximate).

Explanation:

Step1: Identify triangle type

The triangle is right - angled at $B$, so it's a right - triangle with $BC = 2$, $AB=8.77$, and $AC = 9$.

Step2: Use trigonometric ratio

We can use the cosine function to find $\angle C$. In a right - triangle, $\cos C=\frac{adjacent}{hypotenuse}$. The adjacent side to $\angle C$ is $BC = 2$ and the hypotenuse is $AC = 9$. So $\cos C=\frac{BC}{AC}=\frac{2}{9}\approx0.2222$.

Step3: Find the angle

To find the angle whose cosine is approximately $0.2222$, we use the inverse cosine function. $C=\cos^{- 1}(0.2222)\approx77^\circ$ (we can also use the sine function: $\sin C=\frac{AB}{AC}=\frac{8.77}{9}\approx0.9744$, and $\sin^{-1}(0.9744)\approx77^\circ$).

Answer:

$77^\circ$