These are the type of problems that you will be working on in class. These problems are from Lesson 7.

Transcription

1 Pre-Class Problems 10 for Wednesda, October 10 These are the tpe of problems that ou will be working on in class. These problems are from Lesson 7. Solution to Problems on the Pre-Eam. You can go to the solution for each problem b clicking on the problem letter. Objective of the following problems: To take a written description and produce a right triangle with known information and one unknown. The unknown information is represented b a variable. Then use a trigonometric function to obtain an equation containing the variable. Solve this equation for the eact value of the variable. Then approimate the eact value of the variable as indicated. For some of these problems, ou will need the definition for angle of elevation and for angle of depression. An angle of elevation and an angle of depression are both acute angles measured with respect to the horiontal. An angle of elevation is measured upward and an angle of depression is measured downward. The angle below is an angle of elevation from the point A to the point B above. The angle below is an angle of depression from the point B to the point A below. B B A A 1a. The angle of depression from the top of a building to an object on the ground is 40. If the object is 85 feet from the base of the building, then find the height of the building. Find the eact value and then round to the nearest tenth.

2 1b. The angle of depression from the top of a -foot building to an object on the ground is How far is the object from the base of the building? Find the eact value and then round to the nearest hundredth. 1c. From a point P on the ground, the angle of elevation to the top of a -ard tree is 35. What is the distance from the point P to the top of the tree? Find the eact value and then round to the nearest hundredth. 1d. The angle of elevation of the string from the ground to a kite is 48.. If the length of the string is 125 meters, then how far is the kite above ground? Find the eact value and then round to the nearest tenth. 1e. An observer on the ground is ards from the point directl beneath a balloon. If the angle of elevation from the observer to the balloon is 28, then how far is the balloon from the observer? Find the eact value and then round to the nearest hundredth. 1f. A ladder is leaning against the top of a vertical wall. The top of the ladder makes an angle of 34 with the wall. If the height of the wall is meters, then find the length of the ladder. Find the eact value and then round to the nearest tenth. 1g. The angle of elevation from an object on the ground to the top of a building is 57. If the object is 95 meters from the top of the building, then find the distance from the object to the base of the building. Find the eact value and then round to the nearest thousandth. 1h. From a point on the ground which is 40 feet from the base of a tree, the angle of elevation to the top of the tree is What is the height of the tree? Find the eact value and then round to the nearest tenth. 1i. A ladder is leaning against the top of a -ards vertical wall. The bottom of the ladder makes an angle of 24.1 with the ground. How far is the bottom of the ladder from the base of the wall? Find the eact value and then round to the nearest hundredth. Additional problems available in the tetbook: Page , Eamples 7 and 8 starting on page 490. Page Eamples 1, 2, and 3 starting on page 30.

3 Solutions: 1a. Top of Building Object 85 feet NOTE: Since the angle of depression is also , then the angle of elevation is 85 tan tan 40 Answer: Eact: 85 tan 40 ft Approimate: 71.3 ft Back to Problem 1. 1b. Top of Building feet 24.7 Object NOTE: Since the angle of depression is also , then the angle of elevation is

4 tan 24.7 cot 24.7 cot tan 24.7 tan 24.7 tan 24.7 Answer: Eact: cot 24.7 ft Approimate: ft Back to Problem 1. tan 24.7 ft 1c. Top of Tree ards P 35 sin 35 csc 35 csc 35 sin 35 sin 35 sin 35 Answer: Eact: csc 35 d d sin 35 Approimate: d Back to Problem 1.

5 1d. Kite 125 meters sin sin 48. Answer: Eact: 125 sin 48. m Approimate: 93.8 m Back to Problem 1. 1e. Balloon Observer 28 ards cos 28 sec 28 sec 28 cos 28 cos 28 cos 28

6 Answer: Eact: sec 28 d d cos 28 Approimate: d Back to Problem 1. 1f. Top of Wall 34 meters cos 34 sec 34 sec 34 cos 34 cos 34 cos 34 Answer: Eact: sec 34 m m cos 34 Approimate: 7.2 m Back to Problem 1. 1g. Top of Building 95 meters 57 Object

7 95 cos cos 57 Answer: Eact: 95 cos 57 m Approimate: m Back to Problem 1. 1h. Top of Tree feet 40 tan tan Answer: Eact: 40 tan 72.3 ft Approimate: ft Back to Problem 1. 1i. Top of Wall ards 24.1

8 tan 24.1 cot 24.1 cot tan 24.1 tan 24.1 tan 24.1 Answer: Eact: cot 24.1 d Approimate: d Back to Problem 1. tan 24.1 d Solution to Problems on the Pre-Eam: Back to Page 1.. From the top of a building, which is meters tall, the angle of depression to an object on level ground below is.7. How far is the object from the top of the building? Draw a picture and label known information. Indicate an variable ou use. Set up an equation and solve. ( pts.) Top of Building meters.7 Object NOTE: Since the angle of depression is also.7..7, then the angle of elevation is

9 sin.7 csc.7 csc. 7 sin.7 sin.7 sin.7 Answer: csc.7 m sin.7 m