Question

in the right triangle below, tana = 0.45. what is the approximate length of ab? 10 units 13 units 20 units 22 units

Explanation:

Step1: Find the length of \(AC\)

In a right - triangle, \(\tan A=\frac{BC}{AC}\). Given \(\tan A = 0.45\) and \(BC = 9\). Then \(0.45=\frac{9}{AC}\), so \(AC=\frac{9}{0.45}=20\).

Step2: Use the Pythagorean theorem

The Pythagorean theorem states that \(AB^{2}=AC^{2}+BC^{2}\). Substitute \(AC = 20\) and \(BC = 9\) into the formula: \(AB^{2}=20^{2}+9^{2}=400 + 81=481\). Then \(AB=\sqrt{481}\approx22\).

Answer:

22 units