Bell Ringer Please make sure you have turned in your homework (WB pgs. 290-293) in the tray. Please answer the following questions using your notes from yesterday: What is the formula for the Pythagorean Theorem? Who was the Pythagorean Theorem named after? What is the name of the longest side of a right triangle? What is the converse statement of the Pythagorean Theorem?

Today’s Objective: To find and use trigonometric ratios

Essential Understanding Ratios of the side lengths of a right triangle are called trigonometric ratios: Sine, cosine, and tangent You can use the sine, cosine, and tangent ratios to find the measurements of sides and angles of right triangles.

Another way to remember your trig ratios: Some Old Hippy Caught Another Trippin’ On Acid

Problem 1A What are sin A, cos A, and tan A for the triangle shown? A 17 8 B C 15

Problem 1B What are sin, cos, and tan for each acute angle (E and F) using the triangle below? F 15 9 E G 12

You can also use a calculator to find trigonometric ratios You can also use a calculator to find trigonometric ratios. In this Chapter, use Degree mode when finding trigonometric ratios. This allows you to enter angles in degrees.

Problem 2A What is the value of cos 55° to the nearest ten-thousandth? Make sure you have your calculator set to DEGREE mode!

Problem 2B What is the value of each expression listed below? Round your answer to the nearest ten-thousandth. sin 80° tan 45° cos 15° sin 9°

You can use trigonometry to find missing lengths in a right triangle when you know the length of one side and the measure of an acute angle.

Problem 3A To the nearest tenth, what is the value of x in the triangle given below? x 14 48°

Problem 3B To the nearest tenth, what is the value of x in the triangle given below? x 35° 1.575

Problem 3C For each triangle, find the missing side length to the nearest tenth. The hypotenuse is 4m long. How long is the side adjacent to a 40° angle? A 25° angle has an opposite leg 6cm long. How long is the adjacent leg?

If you know the lengths of two sides of a right triangle, you can find a trigonometric ratio for each acute angle of the triangle. If you know a trigonometric ratio for an angle, you can use the inverse of the trigonometric ratio to find the measure of the angle. Use the sinˉ¹, cosˉ¹, or tanˉ¹ feature on your calculator.

Problem 4A What is the measure of each angle in the triangle below? 12 24 C

Problem 4B What is the measure of each angle in the triangle below? A 8 12 C

Problem 4C For each right triangle described, find all three angles to the nearest tenth. The hypotenuse is 8 ft long. The adjacent side is 5 ft long. The adjacent side is 16 mm long. The hypotenuse is 22 mm long.

Today’s assignment Workbook Pg. 311-312 #s 1-40 ALL