(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)
1 point
34 ² + 41² = 2, 837 and √12837= 53.26 m.
34 ² x 41² = 2, 837 and √12837= 121.74 m.
34 x 41 = 2000 and √2000= 121.74 m.
The correct calculation is:
Using the Pythagorean theorem, we can calculate the length of the straight line from A to C, representing the shortest distance if there was a straight path through the pond.
Applying the formula: c^2 = a^2 + b^2
where c is the hypotenuse (the straight line distance), and a and b are the lengths of the other two sides.
In this case, a = 34 m (south) and b = 41 m (east).
So, c^2 = 34^2 + 41^2
c^2 = 1156 + 1681
c^2 = 2837
Taking the square root of both sides:
c = √2837
c ≈ 53.26 m
Therefore, if it were possible to make a way through the pond, approximately 53.26 meters would be saved.
So the correct answer is:
34² + 41² = 2837 and √2837 ≈ 53.26 m.
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 Lily 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 when the 13 ft ladder is leaned against the tree the top of the ladder is even with the ball the distance between the base of the tree and bottom of the ladder is 5 ft how high is the ball industry.
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)
The correct answer is:
The hypotenuse is 13 feet and we are looking for side b. (height of ball in tree)
In this problem, we are given the height of the ladder (hypotenuse), which is 13 ft, and the distance between the base of the tree and the bottom of the ladder (side a), which is 5 ft.
We need to find the height of the ball in the tree (side b).
yea so whats the answer
The answer is:
The hypotenuse is 13 feet and we are looking for side b, which is the height of the ball in the tree.
(3,) What formula can we use to find how high the ball is in the tree?
(1 Point)
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
The correct formula to use in this case is the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
So, the formula to find the height of the ball in the tree (side b) is:
b = √(c^2 - a^2)
In this case, c = 13 ft (length of the ladder) and a = 5 ft (distance between the tree and the bottom of the ladder).
Plugging in these values into the formula, we get:
b = √(13^2 - 5^2)
b = √(169 - 25)
b = √144
b = 12 feet
Therefore, the height of the ball in the tree is 12 feet.
(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)
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
The correct method to find the distance of a straight line from the starting point is to use the Pythagorean theorem.
In this case, Jaya drives north for 9 miles (side a) and then east for 40 miles (side b).
To find the distance of the straight line from the starting point (hypotenuse c), we can use the formula:
c = √(a^2 + b^2)
Plugging in the given values, we get:
c = √(9^2 + 40^2)
c = √(81 + 1600)
c = √1681
c = 41 miles
Therefore, the distance of a straight line from the starting point is 41 miles.
(5.) 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)
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.