# Pythagorean theorem - examples - page 24

- Nonagon

Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm - Find radius

Find radius of circle using pythagorean theorem where a=9, b=r, c= 6+r - Cone 15

The radius of the base of a right circular cone is 14 inches and it's height 18 inches. What is the slant height? - Construct

Construct a rhombus ABCD, if the size of the diagonal AC is 6 cm and diagonal BD 8 cm long. - Pendulum

Calculate the length of the pendulum that is 2 cm lower in the lowest position than in the highest position. The length of the circular arc to be described when moving is 20cm. - Body diagonal - cube

Calculate the surface and cube volume with body diagonal 15 cm long. - Sum of squares

The sum of squares above the sides of the rectangular triangle is 900 cm^{2}. Calculate content of square over the triangle's hypotenuse. - Hyperbola

Find the equation of hyperbola that passes through the point M [30; 24] and has focal points at F1 [0; 4 sqrt 6], F2 [0; -4 sqrt 6]. - Cross road

From the junction of two streets that are perpendicular to each other, two cyclists (each on another street) walked out. One ran 18 km/h and the second 24 km/h. How are they away from a) 6 minutes, b) 15 minutes? - Slant height

The slant height of cone is 5cm and the radius of its base is 3cm, find the volume of the cone - Body diagonal

Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonal. - Right angled triangle 3

Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees - Isosceles triangle

The leg of the isosceles triangle is 5 dm, its height is 20 cm longer than the base. Calculate base length z. - Tangent 3

In a circle with centre O radius is 4√5 cm. EC is the tangent to the circle at point D. Segment AB IS THE DIAMETER of given circle. POINT A is joined with POINT E and POINT B is joined with POINT C. Find DC if BC IS 8cm. - On line

On line p: x = 4 + t, y = 3 + 2t, t is R, find point C, which has the same distance from points A [1,2] and B [-1,0]. - Find the 3

Find the distance and mid-point between A(1,2) and B(5,5). - Rectangular garden

The sides of the rectangular garden are in ratio 1: 2. The diagonal has a length of 20 meters. Calculate the area and perimeter of the garden. - AP RT triangle

The length of the sides of a right triangle form an arithmetic progression, longer leg is 24 cm long. What are the perimeter and area? - A cylinder

A cylinder 108 cm high has a circumference of 24 cm. A string makes exactly 6 complete turns around the cylinder while its two ends touch the cylinder's top and bottom. (forming a spiral around the cylinder). How long is the string in cm? - Diagonals of the rhombus

How long are the diagonals e, f in the diamond, if its side is 5 cm long and its area is 20 cm^{2}?

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Pythagorean theorem is the base for the right triangle calculator.