#12 Algebra 2 Notes Using Trig in Real Life

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1 #12 Algebra 2 Notes 13.1 Using Trig in Real Life

2 #12 Algebra 2 Notes: 13.1 using Trig in Real Life Angle of Elevation Angle of Elevation means you are looking upward and is usually measured from the ground up Angle of Depression Angle of depression means you are looking downward. Note: "The horizontal" means "the ground"

3 Set up an equation and solve each: The angle of elevation of the top of a building from a point 100 ft away from the building on level ground is Find the height of the building. h 100 tan = h 100 h = 100tan h = The height is ft

4 Set up an equation and solve each: [Round to the nearest tenth] 1. A boy flying a kite lets out 300 feet 2. of string which makes an angle of 38 0 with the ground. Assuming that the string is straight, how high above the ground is the kite? A ladder leaning against a wall makes an angle of 74 0 with the ground. If the base of the ladder is 6.5 feet from the wall, how high on the wall is the ladder? h 3.The top of a ladder hits a house 10 meters above the ground while forming a 55 0 angle with the ground. How long is the ladder? 4. A straight road to the top of a hill is 2500 feet long and makes an angle of 12 0 with the horizontal. Find the height of the hill x h

5 5. An airplane climbs at an angle of 11 0 with the ground. Find the ground distance it has traveled when it has attained an altitude of 400 feet. 6. A wire attached to the top of a pole reaches a stake in the ground 20 feet from the base of the pole and makes an angle of 58 0 with the ground. Find the length of the wire. 400 x 11 0 x A 25 foot ladder leans against a building. The ladder's base is 13.5 feet from the building. Find the angle which the ladder makes with the ground A ladder leans against a building. The top of the ladder reaches a point on the building which is 18 feet above the ground. the base of the ladder is 7 ft from the building. Find the measure of the angle which the ladder makes with the level ground

6 9. In order to reach the top of a hill 10. which is 250 ft high, one must travel 2,000 ft straight up a road which leads to the top. Find the measure of the angle the road makes with the horizontal. A monument stands on level ground. The angle of elevation to the top of the monument taken at a point 405 ft away is Find the height of the monument. 11. Find the angle of elevation of the sun when a 24 foot tree casts a 36 foot shadow. 12. A 40 foot ladder is leaning against a building. The base of the ladder is 32 feet from the building. Find the angle that the ladder makes with the building.

7 13. A television tower is 150 feet 14. high and an observer is 120 feet from the base of the tower. Find the angle of elevation to the top of the tower from the place where the observer is standing. A doctor is using a treadmill to assess the strength of a patient's heart. He sets the 48 inch long treadmill at an incline of How high is the end of the treadmill raised? 15. A ladder leaning against a 16. At a point on the ground 50 feet building makes an angle of 78 0 with the ground. The foot of the ladder is 5 feet from the building. How long is the ladder? from the base of a tree, the angle of elevation to the top of the tree is find the height of the tree.

8 #12 Algebra 2 Notes COMPLETED 13.1 Using Trig in Real Life

9 #12 Algebra 2 Notes 13.1 using Trig in Real Life Angle of Elevation Angle of Elevation means you are looking upward and is usually measured from the ground up Angle of Depression Angle of depression means you are looking downward. Note: "The horizontal" means "the ground"

10 Set up an equation and solve each: The angle of elevation of the top of a building from a point 100 ft away from the building on level ground is Find the height of the building. h 100 tan = h 100 h = 100tan h = The height is ft

Set up an equation and solve each: 1. 2. A boy flying a kite lets out 300 feet of string which makes an angle of 38 0 with the ground.

11 Set up an equation and solve each: A boy flying a kite lets out 300 feet of string which makes an angle of 38 0 with the ground. Assuming that the string is straight, how high above the ground is the kite? A ladder leaning against a wall makes an angle of 74 0 with the ground. If the base of the ladder is 6.5 feet from the wall, how high on the wall is the ladder? h 3.The top of a ladder hits a house 10 meters above the ground while forming a 55 0 angle with the ground. How long is the ladder? 4. A straight road to the top of a hill is 2500 feet long and makes an angle of 12 0 with the horizontal. Find the height of the hill x h

12 5. An airplane climbs at an angle of 11 0 with the ground. find the ground distance it has traveled when it has attained an altitude of 400 feet. tan 11 0 = A wire attached to the top of a pole reaches a stake in the ground 20 feet from the base of the pole and makes an angle of 58 0 with the ground. Find the length of the wire. 400 x 11 0 x 58 0 x x tan 11 0 = 400 tan 11 0 tan 11 0 x= ft cos 58 0 = 20 x x cos 58 0 = 20 cos 58 0 cos 58 0 x = 37.7 ft A 25 foot ladder leans against a building. The ladder's base is 13.5 feet from the building. Find the angle which the ladder makes with the ground A ladder leans against a building. The top of the ladder reaches a point on the building which is 18 feet above the ground. the base of the ladder is 7 ft from the building. Find the measure of the angle which the ladder makes with the level ground. tan 0 = 18 7 = tan 1 18 = ( )

13 9. In order to reach the top of a hill 10. which is 250 ft high, one must travel 2,000 ft straight up a road which leads to the top. find the measure of the angle the road makes with the horizontal. A monument stands on level ground. The angle of elevation to the top of the monument taken at a point 405 ft away is Find the height of the monument. 11. Find the angle of elevation of the sun when a 24 foot tree casts a 36 foot shadow tan = = tan = ( ) A 40 foot ladder is leaning against a building. The base of the ladder is 32 feet from the building. Find the angle that the ladder makes with the building. sin = 32 = sin = ( )

14 13. A television tower is 150 feet 14. high and an observer is 120 feet from the base of the tower. Find the angle of elevation to the top of the tower from the place where the observer is standing. tan = = tan = ( ) A doctor is using a treadmill to assess the strength of a patient's heart. He sets the 48 inch long treadmill at an incline of How high is the end of the treadmill raised? 15. A ladder leaning against a 16. At a point on the ground 50 feet building makes an angle of 78 0 with the ground. The foot of the ladder is 5 feet from the building. How long is the ladder? cos 78 0 = 5 x x cos 78 0 = 5 cos 78 0 cos 78 0 x = 24 ft or sin 10 0 = h 48 h = 48 sin 10 0 h = 8.3 inches h = 8.3 in from the base of a tree, the angle of elevation to the top of the tree is find the height of the tree. tan 53 0 = h 50 h = 50 tan 53 0 h = 66.4 ft

Radicals and Pythagorean Theorem Date: Per:

Math 2 Unit 7 Worksheet 1 Name: Radicals and Pythagorean Theorem Date: Per: [1-12] Simplify each radical expression. 1. 75 2. 24. 7 2 4. 10 12 5. 2 6 6. 2 15 20 7. 11 2 8. 9 2 9. 2 2 10. 5 2 11. 7 5 2