D127 Module 2: Math for Elementary Educators

T/F: A triangle with side lengths of 12, 15, and 18 is a right triangle?

False, a triangle with side lengths of 12, 15, and 18 is not a right triangle. It does not satisfy the Pythagorean theorem. 12²+15² ≠ 18² 144+225=369 18²=324. It is a triangle, however, as it satisfies the triangle inequality theorem. 12+15>18

A wire is stabilizing a pole. The wire is 1515 feet long and is 99 feet from the foot of the pole. How tall is the pole? a. 10 feet b. 12 feet c. 15 feet d. 18 feet

The height of the pole is 12 feet. a²+9²=15² a²+81=225 a²=144 a=12

A sailboat has a large sail in the shape of a right triangle. The longest side of the sail measures 2525 yards. The bottom edge of the sail is 77 yards. How tall is the sail? a. 15 yards b. √18 yards c. √32 yards d. 24 yards

The height of the sail is 24 yards. a²+7²=25² a²+49=625 a²=576 a=√576 a=24

A triangle has a leg of 33 and a leg of 44. Find the length of the hypotenuse. a. 5 b. 7 c. 9 d. 11

The length of the hypotenuse is 5. 3²+4²=c² 9+16=c² 25=c² 5=c

A right triangle has a hypotenuse of 1515 and a leg of 99. Find the length of the third side. a. 4 b. 5 c. 12 c. 13

The length of the third side is 12. 9²+b²=15² 81+b²=225 b²=144 b=12

Pythagorean Theorem

a²+b²=c² where a and b represent the legs of a right triangle and c represents the hypotenuse

How far away is the base of the ladder from the side of the wall? A ladder is leaning against the top of a wall that is 12 feet tall. The ladder is 13 feet long. How far away is the base of the ladder from the side of the wall? Assume the wall is perpendicular to the ground. The ladder then is the hypotenuse of a right triangle.

b = 5

Which set of side lengths below form a right triangle? a. (5, 12, 12) b. (5, 12, 13) c. (5, 12, 14) d. (5, 12, 15)

b. (5, 12, 13) 5²+12²=13², which simplifies to 25+144=169 and 169=169

Which is true of ΔABC with m∠C = 90°? a. The triangle has at least two right angles. b. Angles A and B are complementary. c. The shortest side is AB. d. The sum of the interior angles of the triangle is 90.°

b. Angles A and B are complementary. (In a right triangle, the non-right angles are complementary.)

Three sides are given with lengths of 33, 44, and 66. Do these sides form a triangle? Do these sides form a right triangle? a. No, this set of lengths forms neither a triangle nor a right triangle. b. Partly. This set of lengths forms a triangle, but not a right triangle. c. Partly. This set of lengths forms a right triangle, but not a triangle. d. Yes, this set of lengths forms both a triangle and a right triangle.

b. Partly. This set of lengths forms a triangle, but not a right triangle.

Dan left his home and walked 22 miles east and 33 miles north to a museum. What is the straight-line distance from his home to the museum? a. √5 miles b. √13 miles c. 5 miles d. 13 miles

b. √13 miles

In a right triangle, the horizontal distance (one leg) is 6 and the vertical distance (the other leg) is 8. What is the length of the hypotenuse?

10

If the leg lengths are 9 and 12 units, the length of the hypotenuse is ______ units.

15 Using the Pythagorean theorem, 9²+12²=c², and c=15.

If a right triangle has leg lengths of 12 and 16, the length of the hypotenuse is

20

A rubber band has to be stretched on a pegboard between two pegs that are 66 pegs apart left to right and 88 pegs apart top to bottom. How many units (in pegs) must the rubber band be able to stretch in order to join the two pegs? a. √14 b. √28 c. 10 d. 100

6²+8²=c² 36+64=100=c210=c62+82=c² 36+64=100=c² 10=c The rubber band will need to stretch the length of 10 pegs.

In a right triangle, one leg is 6 units long. The hypotenuse is 12 units long. How long is the second leg?

6²+x²=12² 36+x²=144 x²=144−36 x²=108 √x²=√108 x≈10.39

If the hypotenuse is 17 and the length of a leg is 15, the length of the other leg is

8

In a right triangle, the sum of the acute angles is

90°

Which is the correct formula of the Pythagorean theorem? a. a²−b²=c², with a and b as the legs and c as the hypotenuse b. a²−b²=c², with a and c as the legs and b as the hypotenuse c. a²+b²=c², with b and c as the legs and a as the hypotenuse d. a²+b²=c², with a and b as the legs and c as the hypotenuse

d. a²+b²=c², with a and b as the legs and c as the hypotenuse

The longest side in a right triangle is called the

hypotenuse

On a coordinate plane, the length of a right triangle's (hypotenuse, leg, or angle) __________ is found by counting the distance horizontally or vertically.

leg

A hypotenuse is

the largest side of a right triangle, opposite the right angle (only a right triangle has one)

The legs are

the side of a right triangle not opposite the right angle

Pythagorean theorem

the sum of each of the shortest sides squared equals the longest side squared

The horizontal distance corresponds to the _____ axis

x