To find the unknown side length, we can use the Pythagorean theorem. When given two sides of a right triangle, we can square each side, and then add the squares together to find the square of the hypotenuse.
Let's assume the unknown side length is represented by $c$.
Using the Pythagorean theorem: $a^2 + b^2 = c^2$, where $a$ and $b$ are the given side lengths and $c$ is the unknown side length.
In this case, we have $a = 20$ and $b = 30$.
Plugging these values into the equation:
$20^2 + 30^2 = c^2$
$400 + 900 = c^2$
$1300 = c^2$
To find the value of $c$, we can take the square root of both sides:
$\sqrt{1300} = \sqrt{c^2}$
$\sqrt{1300} = c$
Using a calculator, we find that $\sqrt{1300} \approx 36.06$.
Rounding to the nearest hundredth, the unknown side length is approximately $\boxed{36.06}$.
Find the unknown side length in the given triangle. Round to the nearest hundredth.(1 point) one side is 20 one side is 30
7 answers
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.
If Sylvia walks down Johnson Avenue and turns right on 41st Street, she will be walking a total distance of 80 yards on Johnson Avenue and 60 yards on 41st Street.
Therefore, the total distance will be 80 + 60 = 140 yards.
If Sylvia walks through the park, she will be walking a straight line from 42nd Street to 41st Street. We can use the Pythagorean theorem to calculate this distance.
Let the distance in the park be represented by $c$.
Using the Pythagorean theorem: $a^2 + b^2 = c^2$, where $a$ and $b$ are the given side lengths and $c$ is the unknown side length.
In this case, we have $a = 80$ (Johnson Avenue) and $b = 60$ (41st Street).
Plugging these values into the equation:
$80^2 + 60^2 = c^2$
$6400 + 3600 = c^2$
$10000 = c^2$
To find the value of $c$, we can take the square root of both sides:
$\sqrt{10000} = \sqrt{c^2}$
$\sqrt{10000} = c$
Using a calculator, we find that $\sqrt{10000} = 100$.
Therefore, the distance of walking straight through the park is 100 yards.
The distance difference between walking through the park and walking down Johnson Avenue and 41st Street is 140 - 100 = 40 yards.
Therefore, it is $\boxed{40}$ yards shorter for Sylvia to walk through the park.
Therefore, the total distance will be 80 + 60 = 140 yards.
If Sylvia walks through the park, she will be walking a straight line from 42nd Street to 41st Street. We can use the Pythagorean theorem to calculate this distance.
Let the distance in the park be represented by $c$.
Using the Pythagorean theorem: $a^2 + b^2 = c^2$, where $a$ and $b$ are the given side lengths and $c$ is the unknown side length.
In this case, we have $a = 80$ (Johnson Avenue) and $b = 60$ (41st Street).
Plugging these values into the equation:
$80^2 + 60^2 = c^2$
$6400 + 3600 = c^2$
$10000 = c^2$
To find the value of $c$, we can take the square root of both sides:
$\sqrt{10000} = \sqrt{c^2}$
$\sqrt{10000} = c$
Using a calculator, we find that $\sqrt{10000} = 100$.
Therefore, the distance of walking straight through the park is 100 yards.
The distance difference between walking through the park and walking down Johnson Avenue and 41st Street is 140 - 100 = 40 yards.
Therefore, it is $\boxed{40}$ yards shorter for Sylvia to walk through the park.
A triangle has sides a , b , and c . Use the Converse of the Pythagorean Theorem to determine whether a right triangle can be formed if a=16 , b=12 , and c=20 . Option A: Yes, a right triangle can be formed. Option B: No, a right triangle cannot be formed. Choose 1 for Option A or 2 for Option B. (1 point)
To determine whether a right triangle can be formed, we need to check if the given side lengths satisfy the Converse of the Pythagorean Theorem, which states that if the square of the longest side is equal to the sum of the squares of the other two sides, then a right triangle can be formed.
Let's check if the given side lengths satisfy this condition:
If $c = 20$, $a = 16$, and $b = 12$, we have $c^2 = 20^2 = 400$, $a^2 = 16^2 = 256$, and $b^2 = 12^2 = 144$.
Now, we need to check if the sum of the squares of the two smaller sides is equal to the square of the longest side.
$a^2 + b^2 = 256 + 144 = 400$
Since $a^2 + b^2 = c^2$ (400 = 400), the given side lengths of a=16, b=12, and c=20 satisfy the Converse of the Pythagorean Theorem.
Therefore, the answer is Option A: Yes, a right triangle can be formed.
Let's check if the given side lengths satisfy this condition:
If $c = 20$, $a = 16$, and $b = 12$, we have $c^2 = 20^2 = 400$, $a^2 = 16^2 = 256$, and $b^2 = 12^2 = 144$.
Now, we need to check if the sum of the squares of the two smaller sides is equal to the square of the longest side.
$a^2 + b^2 = 256 + 144 = 400$
Since $a^2 + b^2 = c^2$ (400 = 400), the given side lengths of a=16, b=12, and c=20 satisfy the Converse of the Pythagorean Theorem.
Therefore, the answer is Option A: Yes, a right triangle can be formed.
Apply the Pythagorean Theorem to find the unknown side length in the given triangle. Round your answer to the nearest tenth. (1 point) Responses 234 216 14.7 15.3
To apply the Pythagorean Theorem, we can use the equation $a^2 + b^2 = c^2$, where $a$ and $b$ are the given side lengths and $c$ is the unknown side length.
However, the lengths provided in the response do not clearly indicate which side is $a$, which side is $b$, and which side is $c$.
To proceed, please specify which length corresponds to $a$, which one corresponds to $b$, and which one corresponds to $c$.
However, the lengths provided in the response do not clearly indicate which side is $a$, which side is $b$, and which side is $c$.
To proceed, please specify which length corresponds to $a$, which one corresponds to $b$, and which one corresponds to $c$.