# Pythagorean theorem - math word problems

1. 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?
2. IS trapezoid
Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 37 cm, c = |CD| = 29 cm and legs b = d = |BC| = |AD| = 28 cm.
3. Spherical cap
From the sphere of radius 13 was truncated spherical cap. Its height is 6. What part of the volume is spherical cap from whole sphere?
4. Medians
Calculate the sides of a right triangle if the length of the medians to the legs are ta = 21 cm and tb=12 cm.
5. Rhombus
It is given a rhombus of side length a = 29 cm. Touch points of inscribed circle divided his sides into sections a1 = 14 cm and a2 = 15 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus.
6. Cube in a sphere
The cube is inscribed in a sphere with volume 7253 cm3. Determine the length of the edges of a cube.
7. Area 4gon
Calculate area of 4-gon, two and the two sides are equal and parallel with lengths 11, 5, 11 and 5. Inner angles are 45°, 135°,45°, 135°.
8. Laws
From which law follows directly the validity of Pythagoras' theorem in the right triangle? ?
9. Right Δ
A right triangle has the length of one leg 11 cm and length of the hypotenuse 61 cm. Calculate the height of the triangle.
10. Trapezoid MO
The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
11. Proof PT
Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
12. Cuboid
Cuboid with edge a=6 cm and body diagonal u=31 cm has volume V=900 cm3. Calculate the length of the other edges.
13. Square 2
Points D[10,-8] and B[4,5] are opposed vertices of the square ABCD. Calculate area of the square ABCD.
14. Euclid2
In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle.
15. Steps
How many steps you save if you go square estate for diagonal (crosswise), rather than circumvent on the two sides of its perimeter with 307 steps.
16. Square
Points A[-9,7] and B[-4,-5] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD.
17. Triangle
Can be rectangular triangle equilateral?
18. Axial section
Axial section of the cone is an equilateral triangle with area 168 cm2. Calculate the volume of the cone.
19. Diagonal
Determine the dimensions of the cuboid, if diagonal long 53 dm has angle with one edge 42° and with other edge 64°.
20. Right
Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ?

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Pythagorean theorem is the base for the right triangle calculator.