Camila needs to fix the window on the front of her house. The bottom of the window is 16 ft. from the ground. She only has a 20 ft. ladder. How far from the base of the house should she set up the ladder so that the top of the ladder is exactly at the bottom of the window?(1 point)
To find out how much shorter it is for Sylvia to walk through the park, we need to calculate the direct distance from her house to the bank. This can be done using the Pythagorean theorem:
c^2 = a^2 + b^2
Where c represents the direct distance, and a and b are the perpendicular distances between the two street corners.
Given: a = 80 yards, b = 60 yards
c^2 = 80^2 + 60^2 = 6400 + 3600 = 10000
c = √(10000) = 100 yards
Therefore, the direct distance from Sylvia's house to the bank is 100 yards.
Now, we need to determine the distance when she walks through the park. This can be done by subtracting the distances she walks in each direction from 100 yards.
Walking down Johnson Avenue: 100 yards - 60 yards = 40 yards
Turning right on 41st Street: 40 yards - 80 yards = -40 yards (negative value since she is headed in the opposite direction)
Thus, it is 40 yards shorter for Sylvia to walk through the park.
To find the unknown side length in the given triangle, we can use the Pythagorean Theorem:
a^2 + b^2 = c^2
Where a and b are the two legs of the right triangle, and c is the hypotenuse.
Given: a = 3, c = 15
We want to find b.
(3)^2 + b^2 = (15)^2
9 + b^2 = 225
b^2 = 225 - 9
b^2 = 216
Taking the square root of both sides:
b = √216 ≈ 14.7
Therefore, the unknown side length is approximately 14.7.
To find the length of the hypotenuse in a right triangle with legs of 12 cm, we can use the Pythagorean Theorem:
a^2 + b^2 = c^2
Where a and b are the lengths of the legs, and c is the length of the hypotenuse.
Given: a = 12 cm, b = 12 cm
We want to find c.
(12)^2 + (12)^2 = c^2
144 + 144 = c^2
288 = c^2
Taking the square root of both sides:
c = √288 ≈ 16.97
Therefore, the length of the hypotenuse is approximately 16.97 cm.
To find the height that the ladder will reach, we can use the Pythagorean theorem:
a^2 + b^2 = c^2
Where a represents the distance from the base of the ladder to the house, b represents the height the ladder reaches, and c represents the length of the ladder.
Given: a = 6 ft, c = 12 ft
To solve for b:
(6)^2 + b^2 = (12)^2
36 + b^2 = 144
b^2 = 144 - 36
b^2 = 108
Taking the square root of both sides:
b = √108 ≈ 10.4
Therefore, the ladder will reach a height of approximately 10.4 ft.
To find the length of the support cable, we can use the Pythagorean theorem:
a^2 + b^2 = c^2
Where a represents the distance from the base of the pole to the anchor point, b represents the distance from the anchor point to the attachment point on the pole, and c represents the length of the cable.
Given: a = 10 ft, b = 20 ft
To solve for c:
(10)^2 + (20)^2 = c^2
100 + 400 = c^2
c^2 = 500
Taking the square root of both sides:
c = √500 ≈ 22.4
Therefore, the length of the cable is approximately 22.4 ft.
To determine how far from the base of the pole each bracket should be braced in the ground, we can use the Pythagorean theorem:
a^2 + b^2 = c^2
Where a represents the distance from the base of the pole to the brace point, b represents the distance from the brace point to the attachment point on the pole, and c represents the length of the bracket.
Given: b = 4.5 ft, c = 6.5 ft
To solve for a:
a^2 + (4.5)^2 = (6.5)^2
a^2 + 20.25 = 42.25
a^2 = 42.25 - 20.25
a^2 = 22
Taking the square root of both sides:
a = √22 ≈ 4.7
Therefore, each bracket should be braced in the ground approximately 4.7 ft from the base of the pole.
Sylvia likes to walk to work when the weather is nice. She works at the bank at the corner of 41st Street and Edison Avenue. Her house is at the corner of 42nd Street and Johnson Avenue. She can walk down Johnson Avenue and turn right on 41st Street, or she can walk through the park. The distance from 42nd Street to 41st Street is 80 yards, and it is 60 yards from Johnson Avenue to Edison Avenue. Assuming the street intersections are 90° angles, how much shorter is it for Sylvia to walk through the park?
(1 point)
If Sylvia walks through the park instead of straight down Johnson Avenue and straight down 41st Street, the walk will be
yards shorter.
Use the Pythagorean Theorem Quick Check
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Question
Use the image to answer the question.
A right triangle shows the base with a value of 3, the hypotenuse on the left with a value of 15, and the perpendicular side to the base on the right with a question mark.
Apply the Pythagorean Theorem to find the unknown side length in the given triangle. Round your answer to the nearest tenth.
(1 point)
Responses
216
216
14.7
14.7
15.3
15.3
234
If a right triangle has legs that are both 12 cm long, how long is the hypotenuse? Round the answer to the nearest hundredth.(1 point)
Responses
17.0
17.0
288
288
Not enough information is given to solve the problem.
Not enough information is given to solve the problem.
16.97
16.97
Sylvia is replacing a piece of siding on her house. To make the 12 ft. ladder stable, the bottom of the ladder needs to be 6 ft. from the base of her house. Applying the Pythagorean Theorem and rounding to the nearest tenth, how high will the ladder reach so that Sylvia can replace the siding?(1 point)
Responses
10.4 ft.
10.4 ft.
13.4 ft.
13.4 ft.
108 ft.
108 ft.
180 ft.