Pearson Unit 3 Topic 10: Right Triangles and Trigonometry 10-3: Trigonometry Pearson Texas Geometry ©2016 Holt Geometry Texas ©2007

TEKS Focus: (9)(A) Determine the lengths of sides and measures of angles in a right triangle by applying the trigonometric ratios sine, cosine, and tangent to solve problems. (1)(A) Apply mathematics to problems arising in everyday life, society, and the workplace. (1)(F) Analyze mathematical relationships to connect and communicate mathematical ideas.

A trigonometric ratio is a ratio of two sides of a right triangle. Opposite leg O sin A = ---------------- = ----- cos A = ---------------- = ----- tan A = ---------------- = ----- Hypotenuse H Hypotenuse Opposite leg Adjacent leg A Hypotenuse H Adjacent leg Opposite leg O Adjacent leg A

S Soh Cah Toa C T ine OR osine angent You can use the following pneumonic devices to remember the trigonometric ratios: S C T o h a Soh Cah Toa ine OR osine angent djacent ypotenuse pposite ypotenuse pposite djacent

Trigonometric functions can only be used for right triangles. Trigonometric ratios can only be set up for acute angles. In trigonometry, the letter of the vertex of the angle is often used to represent the measure of that angle. For example, the sine of ∡A is written as sin A. Writing Math

Example: 1—in your Flip Book Set up Trig Ratios for the two acute angles in the triangle. Put your answers in fraction form, then in decimal form rounded to the nearest hundredth. sin A cos A tan A Angle A Angle B sin B cos B tan B

Add this diagram in your Flip Book under the example that we just did, and you will also need room to work the problem. 740 m 12 p

Example: 2—not in your Flip Book Set up Trig Ratios for the two acute angles in the triangle. Put your answers in fraction form, then in decimal form rounded to the nearest hundredth. sin A cos A tan A Angle A Angle B sin B cos B tan B 3 5 4

Be sure your calculator is in degree mode, not radian mode. Example: 3—not in your Flip Book Use your calculator to find the trigonometric ratio. Round to the nearest hundredth. sin 52° Be sure your calculator is in degree mode, not radian mode. Caution! sin 52°  0.79

Example: 4—not in your Flip Book Use your calculator to find the trigonometric ratio. Round to the nearest hundredth. tan 65° tan 65°  2.14

Example: 5—not in your Flip Book Use your calculator to find the trigonometric ratio. Round to the nearest hundredth. cos 19° cos 19°  0.95

Caution! Do not round until the final step of your answer. Use the values of the trigonometric ratios provided by your calculator.

Example: 6—in your Flip Book Find the missing angles and missing sides of the triangles. Round angles to the nearest degree and side lengths to the nearest hundredth. Find m∡B = Find h Find g B C D 270 5 g h

Example: 7—in your Flip Book Find the missing angles and missing sides of the triangles. Round angles to the nearest degree and side lengths to the nearest hundredth. Find m∡B = Find x Find y 550 x y 7

Example: 8—add to your Flip Book Find the missing angles and missing sides of the triangles. Round angles to the nearest degree and side lengths to the nearest hundredth. Find m∡A = Find p Find m 740 m 12 p

Example: 9 tan 5 = x . 150 x = 150 (tan 5 ) x = 13.12329953 Suppose someone drops an object from the Leaning Tower of Pisa from a height of 150 ft. How far from the tower will the object land? Round to nearest foot. The angle at the top of the triangle is 5 degrees. tan 5 = x . 150 x = 150 (tan 5 ) x = 13.12329953 The object will land about 13 ft away from the tower

Inverse Trig can be used to find the measure of the acute angles if you have a right triangle and you know two of the sides (either both legs or one leg and the hypotenuse).

If you know that sin A = 5/10 , then . . . How can you find the measure of Angle A using Trigonmetry??? B 5 10 C A If you know that sin A = 5/10 , then . . .

Example: 10 If sin A = .3907, you can find m ∡ A by punching this key sequence on your calculator: = and the answer is ____________. If cos A = .6157, you can find m ∡ A by punching this key sequence on your calculator: = and the answer is ____________. If tan A = 6.3138, you can find m ∡A by punching this key sequence on your calculator: = and the answer

Example: 11—in your Flip Book Solve each right triangle below by finding the missing angles and sides. Round lengths to the nearest hundredth and angle measures to the nearest degree. Note: change the length of BC from 5 in your Flip Book to 4 to match this Example. BA = A =  B =

Example: 12—in your Flip Book Solve each right triangle below by finding the missing angles and sides. Round lengths to the nearest hundredth and angle measures to the nearest degree. EG = = 16 5 =4 5 F =  E = 

Example: 13—in your Flip Book Solve each right triangle below by finding the missing angles and sides. Round lengths to the nearest hundredth and angle measures to the nearest degree. HK = K =  J =