# Pythagorean theorem - math word problems

1. Angle of deviation The surface of the rotating cone is 30 cm2 (with circle base), its surface area is 20 cm2. Calculate the deviation of the side of this cone from the plane of the base.
2. Hexagonal prism The base of the prism is a regular hexagon consisting of six triangles with side a = 12 cm and height va = 10.4 cm. The prism height is 5 cm. Calculate the volume and surface of the prism!
3. Square circles Calculate the length of the described and inscribed circle to the square ABCD with a side of 5cm.
4. Nice prism Calculate the surface of the cuboid if the sum of its edges is a + b + c = 19 cm and the body diagonal size u = 13 cm.
5. Isosceles trapezoid What is the height of an isosceles trapezoid, the base of which has a length of 11 cm and 8 cm and whose legs measure 2.5 cm?
6. Acceleration 2 if a car traveling at a velocity of 80 m/s/south accelerated to a velocity of 100 m/s east in 5 seconds, what is the cars acceleration? using Pythagorean theorem
7. Vertices of RT Show that the points P1 (5,0), P2 (2,1) & P3 (4,7) are the vertices of a right triangle. Show that the quadrilateral with vertices P1(0,1), P2(4,2) P3(3,6) P4(-5,4) has two right triangles.
9. Angles by cosine law Calculate the size of the angles of the triangle ABC, if it is given by: a = 3 cm; b = 5 cm; c = 7 cm (use the sine and cosine theorem).
10. 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?
11. 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)
12. 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.
13. 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.
14. Cube in sphere The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere.
15. Circular segment Calculate the area S of the circular segment and the length of the circular arc l. The height of the circular segment is 2 cm and the angle α = 60°. Help formula: S = 1/2 r2. (Β-sinβ)
16. 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?
18. Square Calculate the perimeter and the area of square with a diagonal length 30 cm.
19. Isosceles triangle Calculate area and perimeter of an isosceles triangle ABC with base AB if a = 6 cm, c = 7 cm.
20. 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.

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Pythagorean theorem is the base for the right triangle calculator.