(1.) To get from point A to point C you must avoid walking through a pond. You must walk 34 m south

Question

and 41 m east. How many meters would be saved if it were possible to make a way through the
pond? Use the digram below to help. Write out the calculations on scrap paper and choose your
final answer! (1 Point)

34^2+41^2=2, 837 and squareroot 2837= 53.26 m
34^2x41^2=2, 837 and squareroot 12837= 121.74 m
34 X 41 =2000 and squareroot 2000= 121.74 m

Answer 1

To find out how many meters would be saved if it were possible to take a direct path (through the pond) from point A to point C rather than walking the longer distance south and east, you can use the Pythagorean theorem.

1. You are walking 34 meters south and 41 meters east. These two legs of the journey form a right triangle where:

   • One leg is 34 m (south)
   • The other leg is 41 m (east)

2. The hypotenuse (the direct distance from point A to point C) can be calculated using the Pythagorean theorem: \[ c = \sqrt{a^2 + b^2} \] where \( a = 34 \) m and \( b = 41 \) m.

3. Now, calculating the hypotenuse: \[ c = \sqrt{34^2 + 41^2} \] \[ = \sqrt{1156 + 1681} \] \[ = \sqrt{2837} \] \[ \approx 53.26 \text{ m} \]

4. Next, we calculate the total distance you are currently walking: \[ \text{Total Distance} = 34 \text{ m (south)} + 41 \text{ m (east)} = 75 \text{ m} \]

5. To find the distance saved by taking the direct route (if possible): \[ \text{Distance Saved} = \text{Total Distance} - \text{Direct Distance} \] \[ = 75 \text{ m} - 53.26 \text{ m} \approx 21.74 \text{ m} \]

Thus, if you could walk directly through the pond, you would save approximately 21.74 meters.

Answer 2

(1.) To get from point A to point C you must avoid walking through a pond. You must walk 34 m south
and 41 m east. How many meters would be saved if it were possible to make a way through the
pond? Use the digram below to help. Write out the calculations on scrap paper and choose your
final answer! (1 Point)

select an answer

1. 34^2+41^2=2, 837 and squareroot 2837= 53.26 m
2. 34^2x41^2=2, 837 and squareroot 12837= 121.74 m
3. 34 X 41 =2000 and squareroot 2000= 121.74 m

Answer 3

To find the correct option, let's analyze the choices in relation to the problem.

You are walking a total distance of:

• 34 m south and 41 m east, which we can use to find the direct distance (the hypotenuse).

Using the Pythagorean theorem:

1. Calculate the squares: \[ 34^2 = 1156 \] \[ 41^2 = 1681 \]

2. Sum these squares: \[ 34^2 + 41^2 = 1156 + 1681 = 2837 \]

3. Taking the square root gives us the hypotenuse: \[ \sqrt{2837} \approx 53.26 \text{ m} \]

The total distance walked around the pond:

• South = 34 m
• East = 41 m
• Total = 34 m + 41 m = 75 m

To find the distance saved if a path directly through the pond was available: \[ \text{Distance saved} = 75 m - 53.26 m = 21.74 m \]

Now looking at your options:

1. 34^2 + 41^2 = 2837 and square root 2837 = 53.26 m (This is correct and reflects the calculations needed for the distance.)
2. 34^2 x 41^2 = 2837 and square root of 12837 = 121.74 m (Incorrect. The multiplication is not part of our calculations.)
3. 34 x 41 = 2000 and square root of 2000 = 121.74 m (Incorrect. The multiplication doesn't help in this context.)

The correct answer is:

1. 34^2 + 41^2 = 2837 and squareroot 2837 = 53.26 m.

Answer 4

Refer to the word problem below. Use this to answer questions 2 & 3.
(2.) What is the hypotonuse (c) in this question? Also, if a= 5 feet, which side do we need to find
? (1 Point)

Wendy and Lilly were playing ball in the yard when the ball got stuck in a tree. It is too high for them to reach, so they need to get a ladder. When the 13 ft. ladder is leaned gaianst the tree, the top of the ladder is even with the ball. the distance betweem the base of the tree and the bottom of the ladder is 5 feet. how high is the ball in the tree?

1 point
The hypotonuse is 13 feet & looking for side c. (distance between ladder & tree)
The hypotonuse is 5 feet and we are looking for side b. (height of ball in tree)
The hypotonuse is 13 feet and we are looking for side b. (height of ball in tree)

Answer 5

To solve the problem, we need to identify the components of the right triangle formed by the ladder, the height of the ball in the tree, and the distance from the base of the tree to the bottom of the ladder.

1. Identifying the sides:

   • The hypotenuse (c) is the length of the ladder, which is 13 feet.
   • The side a is the distance from the base of the tree to the bottom of the ladder, which is 5 feet.
   • We need to find side b, which represents the height of the ball in the tree.

2. Using the Pythagorean theorem: \[ c^2 = a^2 + b^2 \] where:

   • \( c = 13 \) feet (hypotenuse)
   • \( a = 5 \) feet (base)

3. Rearranging to find b: \[ 13^2 = 5^2 + b^2 \] \[ 169 = 25 + b^2 \] \[ b^2 = 169 - 25 \] \[ b^2 = 144 \] \[ b = \sqrt{144} = 12 \text{ feet} \]

So, which answer choice is correct?

• The hypotenuse is 13 feet and we are looking for side b (height of the ball in the tree).

This means the correct answer is:

The hypotenuse is 13 feet and we are looking for side b. (height of the ball in the tree).

Answer 6

(3,) What formula can we use to find how high the ball is in the tree?
(1 Point

13 + 5 = 18 18² = 325 so b=324 feet
13² -5² =169 -25 = 144. and √144= 12 so b=12 feet
13² + 5² =169 + 25 = 194. and √194= 14 so b=14 feet

Answer 7

To find how high the ball is in the tree (which is represented by side \( b \) in the right triangle), we can use the Pythagorean theorem.

The correct approach is to apply the formula:

\[ c^2 = a^2 + b^2 \]

where:

• \( c \) is the length of the hypotenuse (the ladder) = 13 feet,
• \( a \) is the distance from the base of the tree to the ladder = 5 feet,
• \( b \) is the height of the ball in the tree, which we need to find.

From the previous calculations, we derived:

1. Use the Pythagorean theorem: \[ 13^2 = 5^2 + b^2 \]
2. Simplifying: \[ 169 = 25 + b^2 \implies b^2 = 169 - 25 \implies b^2 = 144 \]
3. Taking the square root: \[ b = \sqrt{144} = 12 \text{ feet} \]

Among your provided options, the correct one is:

13² - 5² = 169 - 25 = 144, and √144 = 12, so b = 12 feet.

This correctly represents the method to find how high the ball is in the tree.

Answer 8

(4.) Jaya starts driving north for 9 miles, then takes a right turn, and then he
drives east for another 40 miles. At the end of driving, what is the distance of
a straight line from the starting point? (1 Point)

9 + 40 =49 √49 = 7.2 miles
(40)² - (9)² =1600- 81= 1590 and √1590 = 40 miles
(9)² + (40)² =81 + 1600 = 1681 and √1681 = 41 miles

Answer 9

To find the straight-line distance from Jaya's starting point after driving north and then east, we can use the Pythagorean theorem.

1. Establish the Triangle:

   • Jaya drives 9 miles north (this represents one leg of the triangle).
   • Then he drives 40 miles east (this represents the other leg of the triangle).

2. Use the Pythagorean Theorem: The distance from the starting point to the endpoint forms the hypotenuse of a right triangle: \[ c^2 = a^2 + b^2 \] where:

   • \( a = 9 \) miles (north),
   • \( b = 40 \) miles (east).

3. Calculating the Hypotenuse: \[ c^2 = 9^2 + 40^2 \] \[ = 81 + 1600 \] \[ = 1681 \] \[ c = \sqrt{1681} = 41 \text{ miles} \]

So, the distance of the straight line from the starting point is 41 miles.

Among the presented options, the correct choice is:

(9)² + (40)² = 81 + 1600 = 1681 and √1681 = 41 miles.

Answer 10

question 1. Mary wants to cut across a rectangular lot rather than walk around it.
The lot is 120 feet long and 50 feet wide. Mary walks diagonally across the
lot, how many feet is the short cut? (1 Point)

(50)² + (120)² = 2500 + 14,400= 16,900 and √16,900 = 130 ft
50 + 120 = 170 and √170= 13 ft
(50)² + (120)² = 100+ 240= 340 and √340= 18 feet.

Question 2

(6) Two kids are flying a kite with a string of 50 meters long. If the kids are 35
meters apart, how high is the kite off the ground? What formula should you
use to solve?
Length of the string when in air (c) = 50 meters
The distance of kids apart (b) = 35 meters
The height of the kite off the ground = (a) ?

Use a² + b² = c² to solve. (50)² + (35)²=a²
Use c² - b² = a² to solve. (50)² - (35)² = a²
Just guess!

Answer 11

Question 1

To find the distance Mary would walk diagonally across a rectangular lot, we can use the Pythagorean theorem. The diagonal acts as the hypotenuse.

Given:

• Length of the lot (a) = 120 feet
• Width of the lot (b) = 50 feet

Using the Pythagorean theorem: \[ c^2 = a^2 + b^2 \]

Calculating: \[ c^2 = (50)^2 + (120)^2 \] \[ = 2500 + 14400 \] \[ = 16900 \]

Now take the square root to find the length of the shortcut: \[ c = \sqrt{16900} = 130 \text{ feet} \]

So the correct answer is: (50)² + (120)² = 2500 + 14,400 = 16,900 and √16,900 = 130 ft.

Question 2

In this problem, we want to determine the height of the kite when the string is taut. Here, the kite string acts as the hypotenuse of a right triangle, the distance between the kids forms one leg of the triangle, and the height of the kite forms the other leg.

Given:

• Length of the string when in the air (c) = 50 meters (hypotenuse)
• Distance between kids (b) = 35 meters (one leg)
• Height of the kite off the ground = \(a\) (the other leg, which we need to find)

The relationship between the sides is represented by the Pythagorean theorem, which implies: \[ c^2 = a^2 + b^2 \]

To solve for \(a\), we can rearrange it to: \[ a^2 = c^2 - b^2 \]

Now calculating: \[ a^2 = (50)^2 - (35)^2 \] \[ = 2500 - 1225 \] \[ = 1275 \]

Now, take the square root: \[ a = \sqrt{1275} \approx 35.7 \text{ meters} \]

So the correct method to use is: Use c² - b² = a² to solve. (50)² - (35)² = a².