# Pythagorean theorem - math word problems

1. Forces on earth directions
A force of 60 N [North] and 80 N [East] is exerted on an object wigth 10 kg. What is the acceleration of the object?
2. Right triangle trigonometrics
Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60° and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent)
3. 30-gon
At a regular 30-gon the radius of the inscribed circle is 15cm. Find the "a" side size, circle radius "R", circumference, and content area.
4. Center of gravity
In the isosceles triangle ABC is the ratio of the lengths of AB and the height to AB 10:12. The arm has a length of 26 cm. If the center of gravity T of triangle ABC find area of triangle ABT.
5. Cube in sphere
The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere.
6. Equilateral triangle
The equilateral triangle has a 23 cm long side. Calculate its content area.
The double ladder shoulders should be 3 meters long. What height will the upper top of the ladder reach if the lower ends are 1.8 meters apart?
8. Square
Calculate the perimeter and the area of square with a diagonal length 30 cm.
9. Isosceles triangle
Calculate area and perimeter of an isosceles triangle ABC with base AB if a = 6 cm, c = 7 cm.
10. Billboard
Rectangular billboard is 2.5 m long with a diagonal 2.8 m long. Calculate the perimeter and the content area of the billboard.
11. Land - isosceles trapezoid
Calculate the content and perimeter of the building plot in the form of an isosceles trapezoid with bases 120m, 95m and height 50m.
12. Diagonals of diamond
Find the area and circumference of the diamond ABCD with 15m and 11m diagonals.
13. Two aircraft
From the airport will start simultaneously two planes, which fly tracks are perpendicular to each other. The first flying speed of 680 km/h and the second 840 km/h. Calculate how far the aircraft will fly for half an hour.
4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall?
15. Rhombus
One angle of a rhombus is 136° and the shorter diagonal is 8 cm long. Find the length of the longer diagonal and the side of the rhombus.
16. Rectangular trapezoid
The rectangular trapezoid ABCD is: /AB/ = /BC/ = /AC/. The length of the median is 6 cm. Calculate the circumference and area of a trapezoid.
17. Rectangle
The rectangle has a perimeter 75 cm. Diagonal length is 32.5 cm. Determine the length of the sides.
18. The rope
A 68 centimetre long rope is used to make a rhombus on the ground. The distance between a pair of opposite side corners is 16 centimetres what is the distance between the other two corners?
19. Four sided prism
Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50 degree angle with the base plane.
20. Pentagon
Calculate the length of side, circumference and area of a regular pentagon, which is inscribed in a circle with radius r = 6 cm.

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Pythagorean theorem is the base for the right triangle calculator.