2. Suitcase Diagonal: For a
inch suitcase, the diagonal is approximately 27.39 inches.
3. Right Triangle Leg: In a right triangle with hypotenuse 25 and leg 7, the other leg is 24.
4. Jogging Distance: After running 6 miles north and 9 miles west, the shortest distance back is approximately 10.82 miles.
5. Ladder Height: A 104 ft ladder reaches 96 ft up a wall 40 ft away.
6. Pond Crossing Savings: Walking 10 m south and 24 m east saves approximately 25 m.
7. Rectangle Length: In a rectangle with width 15 inches and diagonal 17 inches, the length is 8 inches.
8. Tent Tallest Point: A tent with slanted sides of 11 ft each and a 12 ft base has a peak height of approximately 12.53 ft.
9. Pole Shadow Distance: A 12 ft pole casts a 16 ft shadow, with 12 ft between the shadow end and the top.
10. Biking Shortest Distance: After biking 33 km south and 56 km west, the shortest distance to the starting point is approximately 64.24 km.
Let's solve each problem one by one:
2. Suitcase Diagonal Length:
- Given a rectangle (the suitcase) with length 22 inches and height 16 inches.
- Using the Pythagorean Theorem:
inches.
3. Right Triangle Leg Length:
- Given a right triangle with hypotenuse 25 and one leg 7.
- Using the Pythagorean Theorem:
units.
4. Shortest Distance Jogging:
- Two legs of the jog form a right triangle with sides 6 miles and 9 miles.
- Using the Pythagorean Theorem:
miles.
5. Ladder Height on Wall:
- Given a ladder with length 104 feet and base 40 feet from the wall.
- Using the Pythagorean Theorem:
feet.
6. Savings by Walking Through the Pond:
- Given a right-angled triangle with legs 10 meters and 24 meters.
- Using the Pythagorean Theorem:
meters.
7. Rectangle Length:
- Given a rectangle with width 15 inches and diagonal 17 inches.
- Using the Pythagorean Theorem:
inches.
8. Tallest Point of the Tent:
- Given a tent with slanted sides of length 11 feet and the bottom 12 feet across.
- Using the Pythagorean Theorem:
feet.
9. Pole Shadow Distance:
- Given a pole with a shadow length of \(16\) feet and a pole length of 12 feet.
- Using similar triangles:
feet.
10. Shortest Distance Biking:
- Two legs of the biking form a right triangle with sides 33 km and 56 km.
- Using the Pythagorean Theorem:
km.
Note: In each solution, the Pythagorean Theorem is used (
) to find the missing side or length.