Find the unknown side length in the given triangle. Round to the nearest hundredth.(1 point)
One side length is 20 and the hypotenuse is 30
We can use the Pythagorean theorem to find the unknown side length in a right triangle. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's denote the unknown side length as x.
According to the Pythagorean theorem, we have:
x^2 + 20^2 = 30^2
Simplifying the equation, we get:
x^2 + 400 = 900
Subtracting 400 from both sides, we have:
x^2 = 500
Taking the square root of both sides, we get:
x = √500
To round to the nearest hundredth, we need to find the decimal approximation of √500.
Using a calculator, we find:
√500 ≈ 22.36
Therefore, the unknown side length is approximately 22.36.
We can use the Pythagorean theorem to find the length of the hypotenuse. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs.
Let's denote the length of the hypotenuse as h.
According to the Pythagorean theorem, we have:
h^2 = 10^2 + 24^2
Simplifying the equation, we get:
h^2 = 100 + 576
h^2 = 676
Taking the square root of both sides, we get:
h = √676
To find the exact length of the hypotenuse, we need to determine the square root of 676.
Using a calculator, we find:
√676 = 26
Therefore, the length of the hypotenuse is 26 cm.
If a right triangle has legs measuring 10 cm and 24 cm, how long is the hypotenuse?(1 point)
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)
We can use the Pythagorean theorem to find the distance from the base of the house to where Camila should set up the ladder.
Let's denote the distance from the base of the house to where she sets up the ladder as x.
According to the Pythagorean theorem, we have:
x^2 + 16^2 = 20^2
Simplifying the equation, we get:
x^2 + 256 = 400
Subtracting 256 from both sides, we have:
x^2 = 144
Taking the square root of both sides, we get:
x = √144
To find the exact distance from the base of the house, we need to determine the square root of 144.
Using a calculator, we find:
√144 = 12
Therefore, Camila should set up the ladder 12 ft away from the base of the house so that the top of the ladder is exactly at the bottom of the window.
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?
To determine how much shorter it is for Sylvia to walk through the park, we need to calculate the distance she would have to walk if she chose the street route and subtract it from the distance she would have to walk if she chose to walk through the park.
Let's denote the distance Sylvia would have to walk if she chose the street route as D_street and the distance she would have to walk if she chose to walk through the park as D_park.
To calculate D_street, we can use the Pythagorean theorem. According to the theorem, in a right triangle, 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, D_street represents the hypotenuse of a right triangle with 80 yards and 60 yards as the other two sides. Therefore, we have:
D_street^2 = 80^2 + 60^2
Simplifying the equation, we get:
D_street^2 = 6400 + 3600
D_street^2 = 10000
Taking the square root of both sides, we get:
D_street = √10000 = 100 yards
So, Sylvia would have to walk 100 yards if she chose the street route.
To calculate D_park, we can use the given information that the distance from 42nd Street to 41st Street is 80 yards, which is the same as D_street. Therefore, D_park = 80 yards.
To determine how much shorter it is for Sylvia to walk through the park, we subtract D_street from D_park:
D_park - D_street = 80 - 100 = -20 yards
Therefore, it is 20 yards shorter for Sylvia to walk through the park.
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 how many yards shorter.
To determine how much shorter it is for Sylvia to walk through the park, we first need to find the distance she would have to walk if she chose the street route and the distance she would have to walk if she chose to walk through the park.
The distance Sylvia would have to walk if she chose the street route can be calculated by adding the distances along each street. She would walk 80 yards from 42nd Street to 41st Street and then 60 yards from 41st Street to Edison Avenue. Therefore, the total distance for the street route is:
Street Distance = 80 yards + 60 yards = 140 yards
To find the distance Sylvia would have to walk if she chose to walk through the park, we can use the Pythagorean theorem. Since Sylvia lives at the corner of 42nd Street and Johnson Avenue and her workplace is at the corner of 41st Street and Edison Avenue, we can consider these as the sides of a right triangle. The distance she would have to walk through the park represents the hypotenuse of this right triangle.
Using the Pythagorean theorem, we have:
Hypotenuse^2 = 80^2 + 60^2
Simplifying the equation, we get:
Hypotenuse^2 = 6400 + 3600
Hypotenuse^2 = 10000
Taking the square root of both sides, we get:
Hypotenuse = √10000 = 100 yards
Therefore, if Sylvia chooses to walk through the park, she would need to walk 100 yards.
To find the difference in distance between the two routes, we subtract the street route distance from the park route distance:
Park Route Distance - Street Route Distance = 100 yards - 140 yards = -40 yards
It is important to note that the negative sign indicates that the park route is shorter than the street route. Therefore, it is 40 yards shorter for Sylvia to walk through the park instead of straight down Johnson Avenue and 41st Street.
To find the unknown side length in a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let's label the unknown side length as "x". Given that one side length is 20 and the hypotenuse is 30, we can set up the equation as follows:
x^2 + 20^2 = 30^2
Simplifying this equation, we have:
x^2 + 400 = 900
Next, we isolate x^2 by subtracting 400 from both sides:
x^2 = 900 - 400
x^2 = 500
To solve for x, we take the square root of both sides:
x = √500
Using a calculator, the square root of 500 is approximately 22.36. Rounding to the nearest hundredth, the unknown side length is approximately 22.36 units.