Right Triangle Trigonometry 7.5-7.6

1. Right TriangleTrigonometry7.5-7.6

2. A trigonometric ratio is a ratio of the lengths of two sides of a right triangle. We will use three different ratios, sine, cosine and tangent.

3. B c a A C b Remember Chief Sohcahtoa

4. A 13 5 B C 12 Examples Using Sohcahtoa: 1. sin A = sin B = cos A = cos B = tan A = tan B =

5. Examples: • Use a calculator. Find the following, rounding to 4 decimal places. • sin 27 = B) tan 32 = C) cos 72 = D) sin 48 = .4540 .6249 .7431 .3090 mode!

6. D I A G H B E F C Examples: • Find the measure of the acute angles given the same trigonometric ratio. A) sin B = B) cos E = C) tan I = 62° X = 67.38 ~ 67° 36.89 ~ 37° inverse function How can I find angles with this???? 2nd sin 15/17

7. Tan 50 = x / 4.8

8. angles of elevation and Depression

9. 7-7 Angles of Elevation and Depression • By definition, the picture at the left shows each of the angle of depression and the angle of elevation. However, since the angles are congruent because ___________________________________, we can just use the triangle at the right the lines are ll, then Alternate Interior angles are congruent

10. Class Exercises: • A surveyor is 130 ft. from a tower. The tower is 86 ft. high. The surveyor’s instrument is 4.75 feet above the ground. Find the angle of elevation. 2. A plane P is 3 miles above ground. The pilot sights the airport A at an angle of depression of 15o. He sights his house H at an angle of depression of 32o. What is the ground distance d between the pilot’s house and the airport. Tan x = (86-4.75)/130 Tan x = 81.25/130 Tan x = .625 X = 32° 86 ft Angle of elevation = ?? 130 ft 4.75 ft Airport distance Tan 15 = 3/a a = 3/tan 15 a = 11.2 miles Home distance Tan 32 = 3/h h = 3/tan 32 h = 4.8 miles 15 32 3 miles 32 15 Airport – home = 11.2 - 4.8 =6.4 miles

11. Q R P Class Exercises: • State an equation that would enable you to solve each problem. Then solve. Round answers to the nearest tenth. • Given mP = 15 and PQ = 37, find QR. b. Given PR = 2.3 and PQ = 5.5, find mP. Sin 15 = x/37 37 * sin 15 = x 9.6 = x Cos P = 2.3/5.5 Cos P = .41818 P = 65.3

12. Class Exercises: • A truck is driven onto a ramp that is 80 ft long. How high is the end of the ramp when the angle of elevation of the ramp is ? ? Sin 30 = x/80 80 * sin 30 = x Sin 45 = x/80 80 * sin 45 = x 80 ft X ft 56.6 Ft = x 40 Ft = x 30

13. Class Exercises: 5. A 6 ft tall person is enjoying a Saturday afternoon by flying a kite. The angle of elevation from him to the kite is . He brought 75 ft of string and has used all of it. How high is the kite? 75 ft x ft 35 Sin 35 = x/75 75 * sin 35 = x 6 ft 43 ft = x The kite is 43 + 6 = 49 ft above the ground.

14. System of equations with trig • You are in a building on the 3rd floor and look across the street at a crane. You notice that the angle when you look up at the top of the crane is 55° and the angle when you look down to the bottom is 61°. If the crane is 60 ft tall, how far away is the building you are in ? Step 1: Write the 2 equations for the system. Step 2: Solve each equation for y=. Step 3: Set the equations equal to each other and solve for x. Step 4: If you need the answer for y plug in the value for x and solve for y. (60-y) 60ft x 55° 61° y ft away from the crane