Question

example 2: find the length of side ab using trig ratios. round your final answer to one decimal place. cosθ = 15 / η cosb = ab = 15×cosb10° = 15×0.9848 = 14.7721 = 15 m

Explanation:

Step1: Identify the cosine - ratio formula

In right - triangle \(ABC\) with right - angle at \(C\), \(\cos B=\frac{BC}{AB}\), where \(BC = 15\)m and \(AB = h\). So, \(\cos B=\frac{15}{h}\).

Step2: Determine the value of \(\cos B\)

Given \(B = 10^{\circ}\), and from the cosine - value table or calculator, \(\cos(10^{\circ})\approx0.9848\).

Step3: Solve for \(AB\)

Since \(\cos B=\frac{15}{AB}\), then \(AB=\frac{15}{\cos B}\). Substituting \(\cos B=\cos(10^{\circ})\approx0.9848\), we get \(AB=\frac{15}{0.9848}\approx15.2\)m.

Answer:

\(15.2\)m