Question

calculate the given angle, to the nearest degree. triangle with legs 33, 44, hypotenuse 55, right - angled, and angle? to find. options: a. 37° b. 53° c. 41° d. 51°

Explanation:

Step1: Use the cosine law

The cosine law formula is \( \cos\theta=\frac{a^{2}+b^{2}-c^{2}}{2ab} \). Let \( a = 33\), \(b = 55\), \(c = 44\). Then \( \cos\theta=\frac{33^{2}+55^{2}-44^{2}}{2\times33\times55} \).
First, calculate \(33^{2}=1089\), \(55^{2}=3025\), \(44^{2}=1936\).
Substitute into the formula: \( \cos\theta=\frac{1089 + 3025-1936}{2\times33\times55}=\frac{4114 - 1936}{3630}=\frac{2178}{3630}=0.6 \).

Step2: Find the angle

Since \( \theta=\cos^{-1}(0.6) \), using a calculator, \( \theta\approx53^{\circ} \).

Answer:

b. \(53^{\circ}\)