Question

1. find the sine, cosine, and tangent angle of a. simplest form fractions. sin a= cos a tan a=

Explanation:

Step1: Find side BC

First, use Pythagoras theorem: $BC = \sqrt{AC^2 - AB^2} = \sqrt{20^2 - 16^2} = \sqrt{400 - 256} = \sqrt{144} = 12$

Step2: Calculate sinA

$\sin A = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{BC}{AC} = \frac{12}{20} = \frac{3}{5}$

Step3: Calculate cosA

$\cos A = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{AB}{AC} = \frac{16}{20} = \frac{4}{5}$

Step4: Calculate tanA

$\tan A = \frac{\text{opposite}}{\text{adjacent}} = \frac{BC}{AB} = \frac{12}{16} = \frac{3}{4}$

Answer:

$\sin A = \frac{3}{5}$, $\cos A = \frac{4}{5}$, $\tan A = \frac{3}{4}$