Lesson Objectives Standards Lesson Notes Lesson Objectives Standards Lesson Notes 8.4 Applications of Rt Triangle Trig After this lesson, you should be able to successfully find and use trigonometric ratios in right triangles. Press the tabs to view details. Press the tabs to view details. Lesson Objectives Standards Lesson Notes G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. G.MG.3 Apply geometric methods to solve design problems. Applications of Rt Trig Make a sketch, show the set up and solve with labels. 1. Mary is flying a kite on a 50 meter string. The string is making a 50 angle with the ground. How high above the ground is the kite? 1
2. Bill is an architect designing a new parking garage for the city. The floors of the garage are to be 10 feet apart. The exit ramps between each pair of floors are to be 75 feet long. What is the measurement of the angle of elevation of each ramp? 10' 75' x 3. A trolley car track rises vertically 40 feet over a horizontal distance of 630 feet. What is the angle of elevation of the track? 4. The length and width of a rectangle are 6 cm and 5 cm, respectively. What is the measure of the angle formed by a diagonal and a longer side? 5. A supporting cable to the top of a 250 feet tower is 300 feet long. What angle does the cable make with the ground? 2
6. A surveyor is 100 meters from a building. He finds that the angle of elevation to the top of the building is 23. If the surveyor's eye level is 1.55 meters above the ground, find the height of the building. 7. To secure a 500 meter radio tower against high winds, guy wires are attached to a ring 5 meters from the top of the tower. The wires form a 15 angle with the tower. Find the distance from the tower to the guy wire anchor in the ground. total height 8. In meteorology, the ceiling is defined as the vertical distance from the ground to the base of the clouds. To measure the ceiling, a spotlight was directed vertically overhead. An observer made the measurements shown in the figure. How high was the ceiling? 9. The boat in the figure is sailing along a straight lake coast. When it is directly opposite a lighthouse (L), the angle between the line of sight from the boat to the lighthouse and to a hotel (H) is 53. Find d, the distance from the boat to shore. 3
10. How far up will the ladder reach? 12 m 11. How high is the kite? 12. A volleyball player spikes the ball from a height of 2.44m. Assume the path of the ball is a straight line. To the nearest degree, what is the maximum angle at which the ball can be hit and land within the court, if the end of the court is 9.4 m away? 100 ft 70 35 13. An escalator in a mall must lift customers to a height of 22 ft. If the angle between the escalator stairs and the ground floor will be 30, what will be the length of the escalator? 14. A skateboard ramp will have a height of 12 in and the angle between the ramp and the ground will be 17. To the nearest tenth of an inch, what will be the length of the ramp? 4
Answers: Sin x = Cos x = Tan x = Place an x in the picture. Write a trig equation and solve. Round distances to the nearest whole number and angles to the nearest degree. 15. A 15 ft wire set at an angle of 25 supports a tree from the top. Find the height of the tree, x. Sin x = Cos x = Tan x = 16. A ship s captain sights the top of a 200 ft cliff at a 17 angle of elevation. How far is the ship from the base of the cliff, x? 17. A scout on top of a 1500 ft mountain spots a campsite. If he measures the angle of depression at 33, how far is the campsite from the foot of the mountain, x? 5
18. A blimp is hovering over the center of a stadium at an altitude of 800 ft. If the radius of the base is 1200 ft, what is his angle of depression to sight the back wall of the stadium? Label the picture, write a trig equation and solve. 19. A 12 ft guy wire is attached to a telephone pole at a point 9.5 ft from the top of the pole. If the wire forms a 51 angle with the ground, how high is the telephone pole? Round to nearest tenth. Label the picture, write a trig equation and solve. 20. If an 8 ft ladder is placed against a building at an angle of 46, how far up the building will the ladder reach? Round answer to the nearest whole number. Answers: 6
Write a trig equation and solve. 21. A fitness trainer set the incline on a treadmill to 7. The walking surface is 5 feet long. Approximately how many inches did the trainer raise the end of the treadmill from the floor? Round your answer to the nearest tenth of a foot. 22. David is building a bike ramp. He wants the angle that the ramp makes with the ground to be 20. If the board he wants to use for his ramp is 3.5 feet long, about how tall will the ramp need to be at the highest point? Round to the nearest tenth. 23. The springboard that Eric uses in his gymnastics class has 6 inch coils and forms an angle of 14.5 with the base. About how long is the springboard? Round to the nearest tenth. 24. The angle of ascent of the first hill of a roller coaster is 55. If the length of the track from the beginning of the ascent to the highest point is 98 feet, what is the height of the roller coaster when it reaches the top of the first hill? Round to the nearest foot. 7
25. Diego used a theodolite to map a region of land for his class in geomorphology. To determine the elevation of a vertical rock formation, he measured the distance from the base of the formation to his position and the angle between the ground and the line of sight to the top of the formation. What is the height of the formation to the nearest meter? 8