1.Rachel drives 33 miles east and then drives 56 miles north. How far is she from her starting point?
23 miles
45 miles
65 miles
2. What is the length of the hypotenuse of the right triangle shown?
A right triangle has one leg labeled 45 cm, the other leg labeled 28 cm, and the hypotenuse labeled c.
35 cm
53 cm
73 cm
89 cm
3. Which right triangle has a hypotenuse of exactly 58 mm?
Three right triangles are shown in a row. The triangle on the left is labeled Triangle A and has legs labeled 35 mm and 23 mm. The triangle in the middle is labeled Triangle B and has legs labeled 50 mm and 30 mm. The triangle on the right is labeled Triangle C and has legs labeled 42 mm and 40 mm.
Triangle A
Triangle B
Triangle C
4. The size of a TV is given by the length of its diagonal, that is, the distance from one corner of the screen to the opposite corner. If a TV has a width of 36 in. and a height of 15 in., what size is the TV?
39 in. TV
43 in. TV
47 in. TV
51 in. TV
The correct answers are:
1. 65 miles
2. 53 cm
3. Triangle C
4. 39 in. TV
1. To find the distance from her starting point, we can use the Pythagorean theorem. The east-west distance is one side of a right triangle, and the north-south distance is the other side. The hypotenuse of this right triangle will be the straight-line distance from her starting point.
Using the Pythagorean theorem, we can calculate the distance as follows:
Distance = √(east-west distance)^2 + (north-south distance)^2
Distance = √(33^2 + 56^2)
Distance = √(1089 + 3136)
Distance = √4225
Distance = 65 miles
So, Rachel is 65 miles away from her starting point.
2. To find the length of the hypotenuse of a right triangle, we can use the Pythagorean theorem. The theorem states that for any right triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse.
Using the Pythagorean theorem, we can calculate the length of the hypotenuse as follows:
c^2 = (leg1)^2 + (leg2)^2
c^2 = 45^2 + 28^2
c^2 = 2025 + 784
c^2 = 2809
c = √2809
c ≈ 53 cm
Therefore, the length of the hypotenuse of the right triangle is approximately 53 cm.
3. To determine which right triangle has a hypotenuse of exactly 58 mm, we can compare the hypotenuse lengths of the three triangles mentioned.
Triangle A has a hypotenuse length of √(35^2 + 23^2) ≈ 41.63 mm.
Triangle B has a hypotenuse length of √(50^2 + 30^2) ≈ 58.31 mm.
Triangle C has a hypotenuse length of √(42^2 + 40^2) ≈ 58.31 mm.
Based on the calculations, Triangle B and Triangle C have a hypotenuse length of approximately 58 mm. However, Triangle C has larger leg lengths and is a better fit for the given hypotenuse measurement of 58 mm.
Therefore, Triangle C has a hypotenuse of exactly 58 mm.
4. To find the size of the TV, we can use the Pythagorean theorem. The width of the TV is one leg of a right triangle, the height is the other leg, and the diagonal is the hypotenuse.
Using the Pythagorean theorem, we can calculate the size of the TV as follows:
Size = √(width)^2 + (height)^2
Size = √(36^2 + 15^2)
Size = √(1296 + 225)
Size = √1521
Size = 39 in. TV
Therefore, the TV size is 39 inches.
1. To find how far Rachel is from her starting point, we can use the Pythagorean theorem because her route forms a right triangle. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the distance from the starting point) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the distance Rachel drives east is one leg of the triangle (33 miles), and the distance she drives north is the other leg (56 miles). So we can calculate the hypotenuse (distance from the starting point) as follows:
Hypotenuse squared = (east distance squared) + (north distance squared)
Hypotenuse squared = (33^2) + (56^2)
Hypotenuse squared = 1089 + 3136
Hypotenuse squared = 4225
To find the length of the hypotenuse, we take the square root of both sides:
Hypotenuse = √4225
Hypotenuse = 65 miles
Therefore, Rachel is 65 miles from her starting point.
2. To find the length of the hypotenuse of a right triangle, we can use the Pythagorean theorem. The theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the legs of the right triangle are labeled as 45 cm and 28 cm. So we can calculate the length of the hypotenuse (labeled c) as follows:
Hypotenuse squared = (leg1 squared) + (leg2 squared)
Hypotenuse squared = (45^2) + (28^2)
Hypotenuse squared = 2025 + 784
Hypotenuse squared = 2809
To find the length of the hypotenuse, we take the square root of both sides:
Hypotenuse = √2809
Hypotenuse = 53 cm
Therefore, the length of the hypotenuse of this right triangle is 53 cm.
3. From the given information, we know that Triangle A has legs of 35 mm and 23 mm, Triangle B has legs of 50 mm and 30 mm, and Triangle C has legs of 42 mm and 40 mm.
To find out which right triangle has a hypotenuse of exactly 58 mm, we can use the Pythagorean theorem. We'll calculate the length of the hypotenuse for each triangle.
For Triangle A:
Hypotenuse squared = (35^2) + (23^2)
Hypotenuse squared = 1225 + 529
Hypotenuse squared = 1754
For Triangle B:
Hypotenuse squared = (50^2) + (30^2)
Hypotenuse squared = 2500 + 900
Hypotenuse squared = 3400
For Triangle C:
Hypotenuse squared = (42^2) + (40^2)
Hypotenuse squared = 1764 + 1600
Hypotenuse squared = 3364
From the calculations, we can see that no triangle has a hypotenuse of exactly 58 mm. Therefore, none of the given triangles (A, B, or C) has a hypotenuse of exactly 58 mm.
4. To find the size of the TV, we can use the Pythagorean theorem again. In this case, the width and height of the TV form a right triangle, and the length of the diagonal (hypotenuse) represents the size of the TV.
Given that the width of the TV is 36 inches and the height is 15 inches, we can calculate the size of the TV as follows:
Hypotenuse squared = (width squared) + (height squared)
Hypotenuse squared = (36^2) + (15^2)
Hypotenuse squared = 1296 + 225
Hypotenuse squared = 1521
To find the size of the TV, we take the square root of both sides:
Hypotenuse = √1521
Hypotenuse = 39 inches
Therefore, the size of the TV is 39 inches.