A right triangle has a hypotenuse of 5 and a side length of 2. Find the angle measurements and the unknown side length. Find the sine, cosine, and tangent for both angles. Without drawing another triangle, compare the trigonometric ratios of [math]\triangle ABC[/math] with those of a triangle that has been dilated by a factor of [math]k = 3[/math].
[list=1] [*]First, draw the triangle with a ruler, and label the side lengths and angles. [*]Find [math]a[/math] by using the Pythagorean Theorem. [*]Use a protractor to measure one of the acute angles, and then use that measurement to find the other acute angle. [*]Find the sine, cosine, and tangent ratios for both acute angles. Express your answer in decimal form to the nearest thousandth. [*]Without drawing a triangle, find the sine, cosine, and tangent for a triangle that has a scale factor of 3 to [math]\triangle ABC[/math]. Compare the trigonometric ratios for the two triangles. [/list] This applet is provided by Walch Education as supplemental material for the [i]CCGPS Analytic Geometry[/i] program. Visit [url="http://www.walch.com"]www.walch.com[/url] for more information on our resources.