# Short cut

Imagine that you are going to the friend. That path has a length 120 meters. Then turn doprava and go another 630 meters and you are at a friend's.

The question is how much the journey will be shorter if you go direct across the field?

Correct result:

x =  108.7 m

#### Solution:

$a=120 \ \text{m} \ \\ b=630 \ \text{m} \ \\ \ \\ c_{0}=a+b=120+630=750 \ \text{m} \ \\ \ \\ c_{1}^2=a^2 + b^2 \ \\ \ \\ c_{1}=\sqrt{ a^2 + b^2 }=\sqrt{ 120^2 + 630^2 } \doteq 30 \ \sqrt{ 457 } \ \text{m} \doteq 641.3267 \ \text{m} \ \\ \ \\ x=c_{0}-c_{1}=750-641.3267=108.7 \ \text{m}$

Try calculation via our triangle calculator.

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Tips to related online calculators
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?
Pythagorean theorem is the base for the right triangle calculator.
Do you want to convert length units?

#### You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem:

## Next similar math problems:

• 1 page
1 page is torn from the book. The sum of the page numbers of all the remaining pages is 15,000. What numbers did the pages have on the page that was torn from the book?
• Two parallel chords
In a circle 70 cm in diameter, two parallel chords are drawn so that the center of the circle lies between the chords. Calculate the distance of these chords if one of them is 42 cm long and the second 56 cm.
• Sailboat
The 20 m long sailboat has an 8 m high mast in the middle of the deck. The top of the mast is fixed to the bow and stern with a steel cable. Determine how much cable is needed to secure the mast and what angle the cable will make with the ship's deck.
• The cube
The cube has a surface area of 216 dm2. Calculate: a) the content of one wall, b) edge length, c) cube volume.
• Concentric circles and chord
In a circle with a diameter d = 10 cm, a chord with a length of 6 cm is constructed. What radius have the concentric circle while touch this chord?
• Height of pyramid
The pyramid ABCDV has edge lengths: AB = 4, AV = 7. What is its height?
• Magnified cube
If the lengths of the edges of the cube are extended by 5 cm, its volume will increase by 485 cm3. Determine the surface of both the original and the magnified cube.
• Trip with compass
During the trip, Peter went 5 km straight north from the cottage, then 12 km west and finally returned straight to the cottage. How many kilometers did Peter cover during the whole trip?
• Derivative problem
The sum of two numbers is 12. Find these numbers if: a) The sum of their third powers is minimal. b) The product of one with the cube of the other is maximal. c) Both are positive and the product of one with the other power of the other is maximal.
• Cube surfce2volume
Calculate the volume of the cube if its surface is 150 cm2.
• Cuboid to cube
A cuboid with dimensions of 9 cm, 6 cm, and 4 cm has the same volume as a cube. Calculate the surface of this cube.
• What is
What is the annual percentage increase in the city when the population has tripled in 20 years?
• Birthdays
In the classroom, students always give candy to their classmates on their birthdays. The birthday person always gives each one candy, and he does not give himself. A total of 650 candies were distributed in the class per year. How many students are in the
• Wallpaper
3750 cm square of wallpaper is needed to glue a cube-shaped box. Can Dad cut out the whole necessary piece of wallpaper as a whole if he has a roll of wallpaper 50 cm wide?
• Diameter = height
The surface of the cylinder, the height of which is equal to the diameter of the base, is 4239 cm square. Calculate the cylinder volume.
• A kite
Children have a kite on an 80m long rope, which floats above a place 25m from the place where children stand. How high is the dragon floating above the terrain?
• Volume of wood
Every year, at the same time, an increase in the volume of wood in the forest is measured. The increase is regularly p% compared to the previous year. If in 10 years the volume of wood has increased by 10%, what is the number p?