4.8 Solving Problems with Trigonometry

1. Sai Thao Xa Thao 4.8Solving Problems with Trigonometry

3. Right Triangle • A triangle in which one angle is equal to 90 is called right triangle. • The side opposite to the right angle is known as hypotenuse. AB is the hypotenuse • The other two sides are known as legs. AC and BC are the legs

4. Video • http://www.youtube.com/watch?v=IovoJ6JEykA • Right click and open hyperlink

5. Example Calculate the length of the side x, given that tan θ = 0.4

6. Example( Words Problems) • A large airplane (plane A) flying at 26,000 feet sights a smaller plane (plane B) traveling at an altitude of 24,000 feet. The angle of depression is 40°. What is the line of sight distance ( x) between the two planes?

7. More Example • A ladder must reach the top of a building. The base of the ladder will be 25′ from the base of the building. The angle of elevation from the base of the ladder to the top of the building is 64°. Find the height of the building (h) and the length of the ladder ( m).

8. Jeopardy of Solving Trigonometry • https://jeopardylabs.com/play/right-triangle-trig3 *Right click, and then go to Open Hyperlink to play the game

9. 10 multiple choice question • 1) Find the length a , b, and c. c 15 30° b A) b=24, c=29.124 B) b=26, c=32.245 C) b=22, c=25.325 D) b=45, c=36.456

10. 2)Find the complement and supplement of the angle. 32° • complement: 54, supplement: 125 b) complement: 58 , supplement:148 c) complement: 48 , supplement: 105 d) complement: 60 , supplement: 165 Solve the problem using geometry 3) Finding a distance- the angle of depression from the top of the smoke town lighthouse 120ft above the surface of the water to a buoy is 10 degree. How far is the buoy from the lighthouse. • A) 680.55ft • B) 721.62ft • C) 669.35 • D) 500.25

11. 4) Finding a guy-wire length- a guy wire connects the top of an antenna to a point on level ground 5ft from the base of the antenna. The angle of elevation formed by this wire is 80°. What are the length of the wire and the height of the antenna? • A) w=28.79ft, h=28.36ft • B) w=25.33ft, h=25.12ft • C) w=29.45ft, h=29.31ft • D) w=24.88ft, h=24.55ft 5) cloud height- to measure the height of a cloud, you place a bright searchlight directly below the cloud and shine the beam straight up. From a point 100ft away from the searchlight, you measure the angle of elevation of the cloud to be 83° 12’. How high is the cloud? a) 925ft b) 853ft c) 900ft d) 839ft

12. 6) architectural design- a barn roof is constructed as shown in the figure. What is the height of the vertical center span? • A) 10.25ft • B) 13.35ft • C) 9.8ft • D) 8.36ft 7) True or false- higher frequency sound waves have shorter periods. 8) Land measure- the angle of depression is 19° from a point 7256 ft above sea level on the north rim of the Grand canyon level to a point 6159 ft above sea level on the south rim. Ho w wide is the canyon at the point. a) 4126ft b) 3265 ft c) 4015ft d) 3186ft

13. 9) Navigation- a shoreline runs north-south, and a boat is due east of the shoreline. The bearings of the boat from two points on the shore are 110° and 100°. Assume the two points are 550 ft apart. How far is the boat from the shore? a) 3012gt b) 2931ft c) 3659ft d) 2954ft 10) Multiple choice- to get a rough idea of the height of a building, John paces off 50 ft from the base of the building, then measures the angle of elevation from the ground to the top of the building at that point to be 58°. About how tall is the building. a) 31 ft b) 42 ft c) 59 ft d) 80 ft e) 417 ft