<p>Geometry 300 Name______Trigonometry 1 Date______</p><p>Today, we are going to begin the study of trigonometry, which means triangle measurement.</p><p>Trigonometric ratios are ratios of the lengths of the sides of right triangles.</p><p>The three most common trigonometric ratios are sine (sin), cosine (cos), and tangent (tan)</p><p>Trigonometric ratios are related to the acute angles of a right triangle NOT the right angle.</p><p>If A and B are the acute angles of a right triangle, complete the following trig ratios…</p><p>Sin A = Sin B =</p><p>Cos A = Cos B =</p><p>Tan A = Tan B =</p><p>Example 1: Find sin M, cos M, tan M, sin N, cos N and tan N. Express each ratio as a fraction. </p><p>6 8</p><p>M 10 N</p><p>Example 2: Find the missing side lengths. Round to the nearest tenth.</p><p> a. b. Geometry 300 Name______Trigonometry 1 Date______Example 3: A 16-foot ladder is propped against a building. The angle it forms with the ground is 55˚. How far up the side of the building does the ladder reach?</p><p>We could also use trig ratios to solve for the acute angles of a right triangle. This involves using the inverse of the trig ratios.</p><p>Example 4: Find the approximate measure of ∠X. X</p><p>8 11</p><p>W Y</p><p>Example 5: Find the missing angle. Round to the nearest tenth.</p><p> a. b. Geometry 300 Name______Trigonometry 1 Date______</p><p>Homework:</p><p>Find the measure of x and y. Round side lengths and angles to the nearest tenth.</p><p>1. 2. </p><p>3. 4. Geometry 300 Name______Trigonometry 1 Date______</p><p>5. 6.</p><p>7. 8. Geometry 300 Name______Trigonometry 1 Date______</p><p>9. A ramp is to be built from a location 4 meters from the base of a loading dock. The dock is 1.2 meters up from the ground. What is the measure of the angle the ramp makes with the ground?</p><p>10. A guy wire is attached to a 100 foot tower that is perpendicular to the ground. The wire makes an angle of 55˚ with the ground. What is the length of the wire?</p>