# Pythagorean theorem - practice problems

#### Number of problems found: 808

- The diamond

The diamond has an area S = 120 cm^{2}, the ratio of the length of its diagonals is e: f = 5: 12. Find the lengths of the side and the height of this diamond. - Woman's day

We can easily make a heart for mothers for Woman's day by drawing two semicircles to the two upper sides of the square standing on their top. What is the radius of the circle circumscribed by this heart when the length of the side of the square is 1? - Side and diagonal

Find the circumference and the area of the rectangle if given: side a = 8 cm diagonal u = 10 cm. - Altitude angles

Cities A, B, C lie in one elevation plane. C is 50 km east of B, B is north of A. C is deviated by 50° from A. The plane flies around places A, B, C at the same altitude. When the aircraft is flying around B, its altitude angle to A is 12°. Find the altit - ABC isosceles

ABC isosceles rights triangle the length or each leg is 1 unit what is the length of the hypotenuse AB in the exact form - The sides

The sides of a right triangle form an arithmetic sequence. The hypotenuse is 24 cm long. Determine the remaining sides of the triangle. - Darnell

Darnell is mountain climbing with Kirk and has just climbed a 9-meter vertical rock face. Kirk is standing at the bottom of the cliff, looking up at Darnell. If Kirk is 15 meters away from Darnell, how far away from the cliff is Kirk standing? - Metal washers

Metal washers with a diameter of 80 mm are cut from a strip of steel sheet with a width of 10 cm and a length of 2 m. Calculate the percentage of material waste if no material is lost when two adjacent circles meet. - Outside point

The square ABCD and the point E lying outside the given square are given. What is the area of the square when the distance | AE | = 2, | DE | = 5 a | BE | = 4? - Right isosceles triangle

What can be the area of a right isosceles triangle with a side length of 8 cm? - Ratio in trapezium

The height v and the base a, c in the trapezoid ABCD are in the ratio 1: 6: 3, its content S = 324 square cm. Peak angle B = 35 degrees. Determine the perimeter of the trapezoid - Arm and base

The isosceles triangle has a circumference of 46 cm. Calculate its area if the arm is 5 cm longer than the base. - Ratio of triangles areas

In an equilateral triangle ABC, the point T is its centre of gravity, the point R is the image of the point T in axial symmetry, along the line AB, and the point N is the image of the point T in axial symmetry along the line BC. Find the ratio of the area - The storm

The top of the 5 m high mast deviated by 1 m from the original vertical axis after the storm. What is the peak now? Round to 2 decimal places. - Garden G

The rectangular, trapezoidal garden has a base length of 81m, 76m, and a vertical arm of 12m. Calculate how many m² of the area will remain for planting greenery if 1/3 of the area is built. Calculate the consumption of mesh for land fencing. - Right triangle

A circle with a radius of 5 cm is described in a right triangle with a 6 cm leg. What is the height at the hypotenuse of this triangle? - Calculate

Calculate the height of an isosceles triangle with base 37.8 mm long and an arm 23.1 mm long. - Is right triangle

Find out if the triangle ABC (with right angle at the vertex C) is right if: a) a = 3dm, b = 40cm, c = 0.5m b) a = 8dm, b = 1.2m, c = 6dm - Rhombus and diagonals

The lengths of the diamond diagonals are e = 48cm, f = 20cm. Calculate the length of its sides. - Ladder

How long is a ladder that touches on a wall 4 meters high, and its lower part is 3 meters away from the wall?

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Pythagorean theorem is the base for the right triangle calculator.