Pythagorean theorem - examples - page 3
- Reverse Pythagorean theorem
Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 77 dm, 85 dm, 36 dm ? Δ DEF: 55 dm, 82 dm, 61 dm ? Δ GHI: 24 mm, 25 mm, 7 mm ? Δ JKL: 32 dm, 51 dm, 82 dm ? Δ MNO: 51 dm, 45 dm, 24 dm ?
- Square diagonal
Calculate length of the square diagonal if the perimeter is 304 cm.
Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ?
Triangle KLM is given by plane coordinates of vertices: K[-12, -11] L[-15, -18] M[-13, -12]. Calculate its area and itsinterior angles.
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.
Right angle prism, whose base is right triangle with leg a = 7 cm and hypotenuse c = 15 cm has same volume as a cube with an edge length of 3 dm. a) Determine the height of the prism b) Calculate the surface of the prism c) What percentage of the cube
- 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.
Calculate volume and surface area of the cone with diameter of the base d = 15 cm and side of cone with the base has angle 52°.
Railways climb 7.4 ‰. Calculate the height difference between two points on the railway distant 3539 meters.
- Spherical cap
From the sphere of radius 18 was truncated spherical cap. Its height is 12. What part of the volume is spherical cap from whole sphere?
- Right triangle
Legs of right are in ratio a:b = 6:8. Hypotenuse has a length of 61 cm. Calculate the perimeter and area of the triangle.
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.
Calculate the length of the side GN and diagonal QN of rectangle QGNH when given: |HN| = 25 cm and angle ∠ QGH = 28 degrees.
- Isosceles right triangle
Calculate the area of an isosceles right triangle whose perimeter is 377 cm.
- Rhombus and inscribed circle
It is given a rhombus with side a = 75 cm and the radius of the inscribed circle r = 36 cm. Calculate the length of its two diagonals.
- R triangle
Calculate the area of a right triangle whose longer leg is 6 dm shorter than the hypotenuse and 3 dm longer than the shorter leg.
From which law follows directly the validity of Pythagoras' theorem in the right triangle? ?
- Floating barrel
Barrel (cylinder shape) floats on water, top of barrel is 8 dm above water and the width of surfaced barrel part is 23 dm. Barrel length is 24 dm. Calculate the volume of the barrel.
Calculate the sides of a right triangle if the length of the medians to the legs are ta = 21 cm and tb=12 cm.
- Rectangle SS
Perimeter of a rectangle is 296 km and its diagonal is 104.74 km. Determine the dimensions of the rectangle.
Pythagorean theorem is the base for the right triangle calculator.