Question

1. examine the figure at right, which is not drawn to scale. which is longer, ab or bc if it was drawn to scale? explain your answer.

Explanation:

Step1: Use trigonometric ratios

In right - triangle \(DBC\), \(\tan C=\frac{DB}{BC}\). Given \(DB = 10\) ft and \(C = 68^{\circ}\), then \(BC=\frac{DB}{\tan C}=\frac{10}{\tan68^{\circ}}\). Since \(\tan68^{\circ}\approx2.475\), \(BC=\frac{10}{2.475}\approx4.04\) ft.
In right - triangle \(DBA\), \(\tan A=\frac{DB}{AB}\). Given \(DB = 10\) ft and \(A = 11^{\circ}\), then \(AB=\frac{DB}{\tan A}=\frac{10}{\tan11^{\circ}}\). Since \(\tan11^{\circ}\approx0.194\), \(AB=\frac{10}{0.194}\approx51.55\) ft.

Answer:

\(AB\) is longer. Because \(AB\approx51.55\) ft and \(BC\approx4.04\) ft.