Question

in the right triangle, tan a = 0.45. what is the approximate length of ab?

Explanation:

Step1: Recall tangent formula

In right - triangle \(ABC\) with right - angle at \(C\), \(\tan A=\frac{BC}{AC}\). Given \(\tan A = 0.45\) and assume \(BC = 9\) (from the figure). Let \(AC=x\), then \(0.45=\frac{9}{x}\).

Step2: Solve for \(AC\)

Cross - multiply: \(0.45x = 9\), so \(x=\frac{9}{0.45}=20\).

Step3: Use Pythagorean theorem

In right - triangle \(ABC\), \(AB^{2}=AC^{2}+BC^{2}\). We know \(AC = 20\) and \(BC = 9\), then \(AB=\sqrt{20^{2}+9^{2}}=\sqrt{400 + 81}=\sqrt{481}\approx22\).

Answer:

22 units