Use the 3 ratios – sin , cos and tan to solve application problems.

1. Solving Word Problems Use the 3 ratios – sin, cos and tan to solve application problems. Choose the easiest ratio(s) to use based on what information you are given in the problem.

2. Depression and Elevation If a person standing on the top of a building looks down at a car on the ground, the angle formed between the line of sight and the horizontal is called the angle of depression. If a person on the ground looks up to the top of a building, the angle formed between the line of sight and the horizontal is called the angle of elevation. horizontal angle of depression line of sight angle of elevation horizontal

3. Balloon Angle of depression Angle of elevation You Angle of Elevation/Depression Sometimes when we use right triangles to model real-life situations, we use the terms angle of elevation and angle of depression. If you are standing on the ground and looking up at a hot air balloon, the angle that you look up from ground level is called the angle of elevation. If someone is in the hot air balloon and looks down to the ground to see you, the angle that they have to lower their eyes, from looking straight ahead, is called the angle of depression.

4. Angle of Elevation/Depression If you look up 15º to see the balloon, then the person in the balloon has to look down 15º to see you on the ground. Angle of elevation = Angle of depression. Balloon Angle of depression = 15º Angle of elevation= 15º You Notice that in this situation, the one of the legs that forms the right angle is also the height of the balloon.

5. 1. From a point 80m from the base of a tower, the angle of elevation is 28˚. How tall is the tower? x 28˚ 80 Using the 28˚ angle as a reference, we know opposite and adjacent sides. Use tan tan 28˚ = 80 (tan 28˚) = x x ≈ 42.5 About 43 m 80 (.5317) = x

6. 2. A ladder that is 20 ft is leaning against the side of a building. If the angle formed between the ladder and ground is 75˚, how far will Coach Jarvis have to crawl to get to the front door when he falls off the ladder (assuming he falls to the base of the ladder)? 20 building ladder 75˚ x Using the 75˚ angle as a reference, we know hypotenuse and adjacent side. Use cos cos 75˚ = 20 (cos 75˚) = x x ≈ 5.2 About 5 ft. 20 (.2588) = x

7. 3. When the sun is 62˚ above the horizon, a building casts a shadow 18m long. How tall is the building? x 62˚ 18 shadow Using the 62˚ angle as a reference, we know opposite and adjacent side. Use tan tan 62˚ = 18 (tan 62˚) = x x ≈ 33.9 About 34 m 18 (1.8807) = x

8. 4. A kite is flying at an angle of elevation of about 55˚. Ignoring the sag in the string, find the height of the kite if 85m of string have been let out. kite 85 x string 55˚ Using the 55˚ angle as a reference, we know hypotenuse and opposite side. Use sin sin 55˚ = 85 (sin 55˚) = x x ≈ 69.6 About 70 m 85 (.8192) = x

9. 5. A 5.50 foot person standing 10 feet from a street light casts a 24 foot shadow. What is the height of the streetlight? 5.5 x˚ 10 14 shadow tan x˚ = x° ≈ 21.45° About 9 ft.

10. 6.The angle of depression from the top of a tower to a boulder on the ground is 38º. If the tower is 25m high, how far from the base of the tower is the boulder? 38º angle of depression 25 Alternate Interior Angles are congruent 38º x Using the 38˚ angle as a reference, we know opposite and adjacent side. Use tan tan 38˚ = 25/x (.7813) = 25/x x ≈ 32.0 About 32 m X = 25/.7813