Solving Word Problems Use the 3 ratios sin

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.

Draw a Picture When solving math problems, it can be very helpful to draw a picture of the situation if none is given. Here is an example. Find the missing sides and angles for Triangle FRY. Given that angle Y is the right angle, f = 68, and y = 88. The picture helps to visualize what we know and what we want to find! 88 r 68

1. From a point 80 m 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 28˚ = 80 (tan 28˚) = x 80 (. 5317) = x x ≈ 42. 5 About 43 m

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)? de r lad building 20 75˚ x Using the 75˚ angle as a reference, we know hypotenuse and adjacent side. Use cos 75˚ = 20 (cos 75˚) = x 20 (. 2588) = x x ≈ 5. 2 About 5 ft.

3. When the sun is 62˚ above the horizon, a building casts a shadow 18 m 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 62˚ = 18 (tan 62˚) = x 18 (1. 8807) = x x ≈ 33. 9 About 34 m

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 85 m of string have been let out. kite x st rin g 85 55˚ Using the 55˚ angle as a reference, we know hypotenuse and opposite side. Use sin 55˚ = 85 (sin 55˚) = x 85 (. 8192) = x x ≈ 69. 6 About 70 m

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 10 14 shadow x˚ tan x˚ = x° ≈ 21. 45° About 9 ft.

Depression and Elevation 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. angle of depression of e lin h sig 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. horizontal t angle of elevation horizontal

6. The angle of depression from the top of a tower to a boulder on the ground is 38º. If the tower is 25 m 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 38˚ = 25/x (. 7813) = 25/x X = 25/. 7813 x ≈ 32. 0 About 32 m