Find the unknown side length in the given triangle. Round to the nearest hundredth.
It's a right triangle, 1 side 20, the other 30.
Here are the answers:
1: 14.7 ft.
2: 16.97 ft.
3: 10.4 ft.
4: 22.4 ft.
5: 4.7 ft.
Those are the quick check answers.
Message to the bot: Thanks! Only 1 answer wrong, awesome. Thanks alot bot (not in a sarcastic way!)!
TUSM!! @Bacon for writing the answers for the quick check! :3
here the answers for the practice:
1. 10.4
2. 22.36
3. 26
4. 12
5. 40
have an amazing night or day.. >_<
Thanks for the help, I'll be back in about 30 seconds to ask some more questions
You're welcome! I'll be here to assist you with any further questions you may have. Take your time, and I'll be ready to help when you return.
Thank you for providing the correct answers! I apologize for the mistake earlier, and I'm glad that I could assist you with your questions. I'm here to help whenever you need it. Thank you for your feedback, and I'm glad I could be of assistance!
To find the unknown side length in a right triangle, we can use the Pythagorean theorem, which 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.
Given that one side length is 20 and the other side length is 30, we can label the unknown side length as x.
Applying the Pythagorean theorem, we have:
x^2 = 20^2 + 30^2
x^2 = 400 + 900
x^2 = 1300
Taking the square root of both sides:
x = √1300
Rounded to the nearest hundredth, the unknown side length is approximately 36.06.
Wrong
Apologies for the mistake. Let's try solving it again.
Given that one side length is 20 and the other side length is 30, we can label the unknown side length as x.
Since it is a right triangle, we can use the Pythagorean theorem:
x^2 = 20^2 + 30^2
x^2 = 400 + 900
x^2 = 1300
Taking the square root of both sides:
x = √1300
To round it to the nearest hundredth, we can use a calculator and get x ≈ 36.06.
Hence, the correct answer is approximately 36.06.
wrong again, its not 36.06
If a right triangle has legs measuring 10 cm and 24 cm, how long is the hypotenuse
To find the length of the hypotenuse in a right triangle, we can again use the Pythagorean theorem.
Given that the legs of the triangle measure 10 cm (let's call it side A) and 24 cm (let's call it side B), we can label the length of the hypotenuse as side C.
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.
Using the formula:
A^2 + B^2 = C^2
Substituting the known values:
10^2 + 24^2 = C^2
100 + 576 = C^2
676 = C^2
To find C, we take the square root of both sides:
C = √676
C = 26
Therefore, the length of the hypotenuse (side C) is 26 cm.
Camilia 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?
To determine how far from the base of the house Camilia should set up the ladder, we can use the Pythagorean theorem in a right triangle formed by the ladder (hypotenuse), the distance from the base of the house to the ladder (one leg), and the height from the ground to the bottom of the window (the other leg).
Let's label the distance from the base of the house to the ladder as x. We can then set up the equation as follows:
x^2 + 16^2 = 20^2
Simplifying:
x^2 + 256 = 400
Subtracting 256 from both sides:
x^2 = 400 - 256
x^2 = 144
Taking the square root of both sides:
x = √144
Since we are dealing with distances, we take the positive square root:
x = 12
Therefore, Camilia should set up the ladder 12 ft 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 hen 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 and turn right on 41st Steet, or she can walk through the park The distance rom 42 Steet to 41 street is 80 yards and it is 60 yards from johnson avenue to edison avenue assuming the street intersections are 90 degree angles how much shorter is it for syvia to walk through the park
To determine how much shorter it is for Sylvia to walk through the park, we need to calculate the length of both paths: one through the streets and the other through the park.
The length of walking through the streets can be calculated by adding the distance from Sylvia's house to the intersection of 41st Street and Johnson Avenue (60 yards) to the distance from the intersection of 41st Street and Johnson Avenue to the bank at the corner of 41st Street and Edison Avenue (80 yards).
Total distance through the streets = 60 yards + 80 yards = 140 yards.
For the path through the park, we can calculate the straight-line distance between Sylvia's house at the corner of 42nd Street and Johnson Avenue and the bank at the corner of 41st Street and Edison Avenue.
Using the Pythagorean theorem:
Distance through the park = √((60 yards)^2 + (80 yards)^2) = √(3600 yards^2 + 6400 yards^2) = √(10000 yards^2) = 100 yards.
Therefore, it is 140 yards to walk through the streets and 100 yards to walk through the park.
To determine how much shorter it is for Sylvia to walk through the park, we can subtract the distance through the park from the distance through the streets:
140 yards - 100 yards = 40 yards.
So, it is 40 yards shorter for Sylvia to walk through the park.
Apply the Pythagorean THeorem to find the unknown side length in the given triangle. Round your answer to the nearest tenth
Certainly, I'm happy to help. For which triangle would you like to find the unknown side length? Please provide the lengths of the known sides or any other information about the triangle.
Of course!
The bottom length is 3, and the side lenth is 15, the other side is unknown
To find the unknown side length in the given triangle, we can use the Pythagorean theorem.
Let's label the unknown side length as x.
According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In this case, we have:
x^2 = 3^2 + 15^2
x^2 = 9 + 225
x^2 = 234
To find x, we take the square root of both sides:
x = √234
Rounded to the nearest tenth, the unknown side length is approximately 15.3.
If a right triangle has legs that are both 12 cm long, how long is the hypotenuse? Round the answer to the nearest hundredth
To find the length of the hypotenuse in the given right triangle, we can use the Pythagorean theorem.
Let's label the length of both legs as 12 cm. We can call these legs side A and side B, and the length of the hypotenuse as side C.
According to the Pythagorean theorem, 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, we have:
C^2 = 12^2 + 12^2
C^2 = 144 + 144
C^2 = 288
To find C, we take the square root of both sides:
C = √288
Rounded to the nearest hundredth, the length of the hypotenuse is approximately 16.97 cm.
Sylvia is replacing a peice 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 with the ladder reach so that Sylvia can replace the siding?
To determine how high the ladder will reach when Sylvia replaces the siding, we can use the Pythagorean theorem.
Let's label the height the ladder reaches as 'h'.
According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (ladder) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the length of the ladder (hypotenuse) is 12 ft, and the distance from the base of the ladder to the house is 6 ft.
We can set up the equation as follows:
h^2 + 6^2 = 12^2
Simplifying:
h^2 + 36 = 144
Subtracting 36 from both sides:
h^2 = 108
To find 'h', we take the square root of both sides:
h = √108
Rounded to the nearest tenth, the ladder will reach approximately 10.4 ft high.
Therefore, Sylvia can use the ladder to reach a height of approximately 10.4 ft to replace the siding on her house.
An electric pole has a support cable that is attached to the pole 20 ft. from the ground. The cable is anchored on the ground 10 ft from the base of the pole. How long is the cable? Round to the nearest tenth.
To find the length of the support cable, we can use the Pythagorean theorem.
Let's label the length of the cable as 'c'.
According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the cable) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the distance from the ground to where the cable is attached to the pole is 20 ft, and the distance from the base of the pole to where the cable is anchored on the ground is 10 ft.
We can set up the equation as follows:
c^2 = 20^2 + 10^2
Simplifying:
c^2 = 400 + 100
c^2 = 500
To find 'c', we take the square root of both sides:
c = √500
Rounded to the nearest tenth, the length of the cable is approximately 22.4 ft.
Therefore, the cable is approximately 22.4 ft long.
A streetlight post needssome extra support for potential bad weather and high winds. The city wants to install metal support brackets on the light post. Each bracket with be braced into the ground and will then attach to a point on the pole that is 4.5 ft. from the ground. Each bracked is 6.5 ft long. How far from the base of the pole should eache braket be braced in the ground? Round to the nearest tenth.
To determine how far from the base of the pole each bracket should be braced in the ground, we can use the Pythagorean theorem.
Let's label the distance from the base of the pole to each bracket as 'x'.
According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the bracket) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the distance from the ground to the point on the pole where the bracket is attached is 4.5 ft, and the length of the bracket is 6.5 ft.
We can set up the equation as follows:
x^2 + 4.5^2 = 6.5^2
Simplifying:
x^2 + 20.25 = 42.25
x^2 = 42.25 - 20.25
x^2 = 22
To find 'x', we take the square root of both sides:
x = √22
Rounded to the nearest tenth, each bracket should be braced in the ground approximately 4.7 ft from the base of the pole.
Therefore, each bracket should be braced in the ground approximately 4.7 ft from the base of the pole.
Apologies once again for the mistake. Let's solve it correctly this time.
Given that one side length is 20 (let's call it side A) and the other side length is 30 (let's call it side B), we can label the unknown side length as side C.
Since it is a right triangle, we can use the Pythagorean theorem:
A^2 + B^2 = C^2
Substituting the known values:
20^2 + 30^2 = C^2
400 + 900 = C^2
1300 = C^2
To find C, we take the square root of both sides:
C = √1300
C ≈ 36.06
So the approximate unknown side length (C) is 36.06. Apologies for the confusion earlier.