Pythagorean theorem.
find the unknown side length in the given triangle round to the nearest hundred
a right triangle with 20 and 30 on each lengths
To find the unknown side length in a right triangle using the Pythagorean theorem, we can use the formula a^2 + b^2 = c^2, where a and b are the lengths of the two known sides, and c is the length of the hypotenuse.
In this case, the two known side lengths are 20 and 30.
Let's substitute these values into the formula:
20^2 + 30^2 = c^2
400 + 900 = c^2
1300 = c^2
To find the value of c, we can take the square root of both sides of the equation:
√(1300) = √(c^2)
36.06 = c
Rounding the answer to the nearest hundred, we get approximately c = 36.
a right triangle with one length being 20 and the other being 30
Let's assume that the side length of 20 is one of the legs of the right triangle, and the side length of 30 is the hypotenuse.
Using the Pythagorean theorem, we have:
a^2 + b^2 = c^2
Where a and b are the lengths of the legs, and c is the length of the hypotenuse.
Plugging in the given values:
20^2 + b^2 = 30^2
400 + b^2 = 900
To isolate b^2, we subtract 400 from both sides:
b^2 = 900 - 400
b^2 = 500
To find b, we can take the square root of both sides:
b = √(500)
b ≈ 22.36
Therefore, the unknown side length of the right triangle is approximately 22.36. Rounding to the nearest hundred would give us 22 as the answer.
with the Pythagorean theorem?
I apologize for the previous response. Let's solve the problem using the Pythagorean theorem.
We are given that one side of the right triangle is 20 and the other side is 30. Let's label the unknown side as x.
According to the Pythagorean theorem:
a^2 + b^2 = c^2
Substituting the given values:
20^2 + x^2 = 30^2
400 + x^2 = 900
Subtracting 400 from both sides:
x^2 = 900 - 400
x^2 = 500
To find x, we can take the square root of both sides:
x = √500
x ≈ 22.36
Therefore, the unknown side length in the right triangle is approximately 22.36. Rounding to the nearest hundred would still give us 22 as the answer.
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 to Johnson Avenue and turn right on 41st street, or she can walk through the park. The distance from 42nd 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?
answer using pythagorean theorem
To find out how much shorter it is for Sylvia to walk through the park, we can use the Pythagorean theorem.
Let's consider the two options:
Option 1: Walking down to Johnson Avenue and turning right on 41st street.
Option 2: Walking through the park.
In both options, we have a right triangle where the two legs represent the distances Sylvia walks and the hypotenuse represents the shortest distance between her house and work.
For Option 1:
One leg is the distance from Sylvia's house to Johnson Avenue, which is 80 yards.
The other leg is the distance from Johnson Avenue to Edison Avenue, which is 60 yards.
Let's label the hypotenuse as a.
According to the Pythagorean theorem:
80^2 + 60^2 = a^2
6400 + 3600 = a^2
10000 = a^2
To find a, we can take the square root of both sides:
√10000 = √(a^2)
100 = a
So, for Option 1, the shortest distance between Sylvia's house and work is 100 yards.
For Option 2 (walking through the park):
One leg is the distance from Sylvia's house to 42nd street, which is also 80 yards.
The other leg is the distance from 42nd street to 41st street, which is 60 yards.
Let's label the hypotenuse as b.
According to the Pythagorean theorem:
80^2 + 60^2 = b^2
6400 + 3600 = b^2
10000 = b^2
To find b, we take the square root of both sides:
√10000 = √(b^2)
100 = b
So, for Option 2 (walking through the park), the shortest distance between Sylvia's house and work is also 100 yards.
Therefore, the two options have the same shortest distance of 100 yards, so there is no difference in distance between the two routes.
my source says your incorrect, please provide all possible answers
I apologize for the confusion. Let's reassess the problem and provide all possible answers.
Option 1: Walking down to Johnson Avenue and turning right on 41st street.
As mentioned before, one leg is the distance from Sylvia's house to Johnson Avenue, which is 80 yards, and the other leg is the distance from Johnson Avenue to Edison Avenue, which is 60 yards. Let's label the hypotenuse as a.
Using the Pythagorean theorem:
80^2 + 60^2 = a^2
6400 + 3600 = a^2
10000 = a^2
Taking the square root of both sides:
√10000 = √(a^2)
100 = a
So, for Option 1, the shortest distance between Sylvia's house and work is 100 yards.
Option 2: Walking through the park.
One leg is the distance from Sylvia's house to 42nd street, which is 80 yards, and the other leg is the distance from 42nd street to 41st street, which is 60 yards. Let's label the hypotenuse as b.
Using the Pythagorean theorem:
80^2 + 60^2 = b^2
6400 + 3600 = b^2
10000 = b^2
Taking the square root of both sides:
√10000 = √(b^2)
100 = b
So, for Option 2 (walking through the park) as well, the shortest distance between Sylvia's house and work is 100 yards.
Therefore, based on the given information, both routes have the same shortest distance of 100 yards. I apologize if there was any confusion previously.
apply for pythagorean the theorem to find the unknown side length in the given triangle about your answer to the nearest ten
(the image shows of right triangle with one side having 15 as a length and the other side having 3 as a length)
A.234
B.14.7
C.15.3
D.216
To find the unknown side length in a right triangle using the Pythagorean theorem, we can use the formula a^2 + b^2 = c^2, where a and b are the lengths of the two known sides, and c is the length of the hypotenuse.
In this case, one side of the right triangle has a length of 15, and the other side has a length of 3. Let's label the unknown side as x.
Using the Pythagorean theorem:
3^2 + 15^2 = x^2
9 + 225 = x^2
234 = x^2
To find x, we can take the square root of both sides of the equation:
x = √234
Rounding to the nearest ten, we get approximately x = 14.7.
Therefore, the answer is B.14.7.
if a right triangle has legs that are both 12 cm long how long is the hypotenuse? round the answer to the nearest hundredth
(pythagorean theorem is to be applied to all questions)
A.1697
B.17.0
C.not enough information is given to solve the problem
D. 288
To find the length of the hypotenuse in a right triangle using the Pythagorean theorem, we can use the formula a^2 + b^2 = c^2, where a and b are the lengths of the two legs, and c is the length of the hypotenuse.
In this case, both legs of the right triangle have a length of 12 cm. Let's label the hypotenuse as c.
Using the Pythagorean theorem:
12^2 + 12^2 = c^2
144 + 144 = c^2
288 = c^2
To find c, we can take the square root of both sides:
c = √288
Rounding the answer to the nearest hundredth, we get approximately c = 16.97.
Therefore, the answer is A.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 replace the siding?
To determine how high the ladder will reach when Sylvia replaces the siding, we can apply the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
Let's label the height that the ladder will reach as 'h'. The distance from the base of her house to the bottom of the ladder is 6 ft, and the length of the ladder is 12 ft.
Using the Pythagorean theorem:
6^2 + h^2 = 12^2
36 + h^2 = 144
h^2 = 144 - 36
h^2 = 108
To find 'h', we can take the square root of both sides:
h = √108
h ≈ 10.4
Therefore, the ladder will reach approximately 10.4 ft high when Sylvia replaces the siding.
A steel light potion needs some extra support for potential bad weather and High winds. The city wants to install metal support brackets on the light post. Each bracket is 6.5 ft. Long. How far from the base should each bracket be braced in the ground? Round to the nearest tenth.
(Pythagorean theorem)
A.22.0
B.62.5
C.4.7
D7.9
To determine how far from the base each bracket should be braced in the ground, we can apply the Pythagorean theorem.
Let's label the distance from the base to the brace point on the ground as 'x'. The length of the metal support bracket is given as 6.5 ft.
Using the Pythagorean theorem:
x^2 + 6.5^2 = 12^2
x^2 + 42.25 = 144
x^2 = 144 - 42.25
x^2 = 101.75
To find 'x', we can take the square root of both sides:
x = √101.75
x ≈ 10.1
Therefore, each bracket should be braced approximately 10.1 ft from the base in the ground. Rounding to the nearest tenth, the answer is not provided in the options given. However, the closest option to 10.1 is option A, which is 22.0.