Question

1. cos a

c 30 a
24
b 18
a) 3/5 b) 5/4
c) 3/4 d) 4/3

Explanation:

Step1: Use Pythagorean theorem to find \(AB\)

In right - triangle \(ABC\) with \(\angle B = 90^{\circ}\), by Pythagorean theorem \(AC^{2}=AB^{2}+BC^{2}\). Given \(BC = 24\), \(AB=18\), then \(AC=\sqrt{24^{2}+18^{2}}=\sqrt{576 + 324}=\sqrt{900}=30\) (already given in the problem).

Step2: Use the cosine formula

The cosine of an angle in a right - triangle is defined as \(\cos A=\frac{adjacent}{hypotenuse}\). For \(\angle A\), the adjacent side to \(\angle A\) is \(AB = 18\) and the hypotenuse is \(AC=30\). So \(\cos A=\frac{AB}{AC}=\frac{18}{30}=\frac{3}{5}\)

Answer:

A. \(\frac{3}{5}\)