The document contains 15 questions applying the Pythagorean theorem and special right triangles to solve problems involving lengths and distances. It asks the reader to calculate distances, lengths, heights and costs given information like measurements of sides of shapes or angles of inclination. The questions cover a range of real-world scenarios involving structures, ladders, ropes, trees and more.

1. APPLICATIONS OF THE PYTHAGOREAN THEOREM

2. Question #1 What is the length of the diagonal of a rectangle whose sides measure 4 and 6? 213

3. Question #2 If the diagonal of a rectangle measures 10 cm and one of its sides measure 8 cm, determine the length of the other side. 6 cm

4. Question #3 What is the measure of the diagonal of a square with a side length of 28 cm? 142 cm

5. Question #4 Calculate the length of the side of a square whose diagonal measures 8 cm. 4 cm

6. Question #5 A 5 m ladder is 4 m from the base of a wall. How high up the wall does the ladder reach? 3 m

7. Question #6 The distance between the base of the Leaning Tower of Pisa and the top of the tower is approximately 54 m. The tower is leaning about 4 m from the perpendicular. What is the distance of the top of the tower from the ground? 1029 m

8. Question #7 A flagpole is 12 m high. Wire supports attached to the tip of the flagpole are 5 m away from its base. Find the length one wire support. 13 m

9. Question #8 A tower 15 m high is to be braced by three wires that are attached to the ground 8 m from the base of the tower. If the wire costs P100 per meter, how much would the total wiring cost? P5,100

10. Question #9 A baseball diamond is a square that measures 90 ft on a side. How far must the catcher throw a ball from the homebase to the 2nd base?

11. Question #10 In a right triangle, the hypotenuse is 17 cm. The measure of one leg is one less than twice the measure of the other. Determine the length of measure of both legs. 8ft and 15 ft

12. Question #11 The diagonal of a rhombus are perpendicular bisectors of each other. If the diagonals of a certain rhombus measures 10 cm and 24 cm, find the length of one side. 13 cm

13. Question #12 The measure of the side of a rhombus is 10 mm and the measure of one of its diagonals is 16 mm. What is the length of the other diagonal? 12 mm

14. Question #13 What is the measure of the longest stick we can put inside a 3 m x 4 m x 5 m box? 52 m

15. Question #14 The length of the hypotenuse is three more than twice the length of the shortest side. The length of the other leg is two more than twice the shortest side. Find the length of the hypotenuse. 13

16. Question #15 Mr. Evardone wants to install his newly acquired air-conditioning unit. The front of the unit is rectangular in shape and its diagonal measures 25 inches. He cuts a hole in the wall that measures 20 inches by 15 inches. Did Mr. Evardone cut the right hole? ?

17. Question #15 Legolas is chasing after an orc. The orc climbs up a vertical wall to escape. Legolas needs to remove a piece of brick that will make the wall collapse. To remove the brick, he must shoot his arrow with a length of rope tied to the arrow and then pull the rope. Will the rope escape if the rope is just 35 meters long? ?

18. Question #15 A helicopter is, 545 ft. directly above one end of Lake Unipag. A spy who is 55 ft directly across the lake, wants to plant a homing device on the chopper. If his homing device launcher can shoot with a straight path, what distance will the device travel? ?

19. Question #15 A 24 ft ladder will be used to paint a house. If the foot of the ladder must be placed 4 ft from the house to avoid the flowers and shrubs, what is the highest point on the house that the ladder could reach? ?

20. Question #15 A faucet is located in a corner of a rectangular lot that measures 30 ft by 45 ft. What is the minimum length of a garden hose in order to reach all parts of the lot? Assume the water from the hose could water plants 5 ft from the hose. ?

21. Question #15 A tower 13.5 m high is to be braced by four wires that are attached to the ground 3.5 m from the base of the tower. If the wire costs PhP 120 per meter, how much would the wire cost? ?

23. APPLICATION OF THE SPECIAL RIGHT TRIANGLES

24. Question #1 Tony Hawk skates from the top of a ramp with an angle of inclination of 30o. The height of the ramp is 6 meters. Find the distance he skated until he reaches the bottom of the ramp. 8 m

25. A bird on top of a tree saw an earthworm on the ground. The angle of depression from the bird to the worm is 60o. If the tree is 10 meters high, how far is the worm from the bird? Question #2 Question #3

26. Question #3 A 20 foot ladder just reaches the top of the wall with an angle of inclination of 30o. How tall is the wall? 10ft

27. Question #10 How high would a 10 ft ladder reach a side of a building, if the ladder is set 60o above the ground?

28. Question #10 A bird on the top of a tree saw an earthworm on the ground. The angle of depression from the bird to the worm is 60°. If the tree is 7.5 meters high, how far is the worm from the bird? ?

29. Question #10 A 20 foot ladder just reaches the top of the wall with an angle of elevation of 30°. How tall is the wall? ?

30. Question #10 How high would a 10 ft ladder reach a side of the building, if the ladder is set 60° above the ground? ?

31. Question #10 Rhoel sees ripe mangoes in Jupiter’s tree and want to pick them. He uses a 15 ft long bamboo stick, at an angle of 60°, to poke the mangoes to let it fall. If Rhowl is 5 ft 9 inches tall, how high was the mangoes from the ground? ?