# Pythagorean theorem - math word problems

#### Number of problems found: 655

• Rectangle The rectangle is 21 cm long and 38 cm wide. Determine the radius of the circle circumscribing rectangle.
• Segment Calculate the length of the segment AB, if the coordinates of the end vertices are A[10, -4] and B[5, 5].
• RT and ratio A right triangle whose legs are in a ratio 6:12 has hypotenuse 68 m long. How long are its legs?
• Square side Calculate length of side square ABCD with vertex A[0, 0] if diagonal BD lies on line p: -4x -5 =0.
• Vector Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2).
• Arm Calculate the length of the arm r of isosceles triangle ABC, with base |AB| = 14 cm and a height v=18 cm.
• Distance Calculate distance between two points X[18; 19] and W[20; 3].
• 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.
• Circle chord Determine the radius of the circle in which the chord 6 cm away from the center of the circle is 12 cm longer than the radius of the circle.
• Euklid4 Legs of a right triangle have dimensions 244 m and 246 m. Calculate the length of the hypotenuse and the height of this right triangle.
• 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?
• Spherical cap What is the surface area of a spherical cap, the base diameter 20 m, height 2 m.
• Horizon The top of a lighthouse is 19 m above the sea. How far away is an object which is just “on the horizon”? [Assume the earth is a sphere of radius 6378.1 km.]
• Prism The lenght, width and height of a right prism are 17, 11 and 11 respectively. What is the lenght of the longest segment whose endpoints are vertices of the prism?
• River From the observatory 11 m high and 24 m from the river bank, river width appears in the visual angle φ = 13°. Calculate width of the river.
• Circles In the circle with a radius 7.5 cm are constructed two parallel chord whose lengths are 9 cm and 12 cm. Calculate the distance of these chords (if there are two possible solutions write both).
• Chord - TS v2 The radius of circle k measures 87 cm. Chord GH = 22 cm. What is TS?
• Rhombus Calculate the length of the diagonal AC of the rhombus ABCD, if its perimeter is 84 dm and the other diagonal BD has length 20 dm.
• Tetrahedral pyramid What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=16 and height v=16?
• RT 10 Area of right triangle is 84 cm2 and one of its cathethus is a=10 cm. Calculate perimeter of the triangle ABC.

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Pythagorean theorem is the base for the right triangle calculator.