# Angle + Pythagorean theorem - math problems

1. Triangular prism Calculate the surface of a regular triangular prism, the edges of the base are 6 cm long and the height of the prism is 15 cm.
2. Right angle If a, b and c are two sides of a triangle ABC, a right angle in A, find the value on each missing side. If b=10, c=6
3. Angle of the body diagonals Using vector dot product calculate the angle of the body diagonals of the cube.
4. Five-gon Calculate the side a, the circumference and the area of the regular 5-angle if Rop = 6cm.
5. What percentage What percentage of the Earth’s surface is seen by an astronaut from a height of h = 350 km. Take the Earth as a sphere with the radius R = 6370 km
6. Top of the tower The top of the tower has the shape of a regular hexagonal pyramid. The base edge has a length of 1.2 m, the pyramid height is 1.6 m. How many square meters of sheet metal is needed to cover the top of the tower if 15% extra sheet metal is needed for joint
7. Hexagonal pyramid Calculate the surface area of a regular hexagonal pyramid with a base inscribed in a circle with a radius of 8 cm and a height of 20 cm.
8. Triangular pyramid A regular tetrahedron is a triangular pyramid whose base and walls are identical equilateral triangles. Calculate the height of this body if the edge length is a = 8 cm
9. Wall height Calculate the height of a regular hexagonal pyramid with a base edge of 5 cm and a wall height w = 20 cm.
10. Cone side Calculate the volume and area of the cone whose height is 10 cm and the axial section of the cone has an angle of 30 degrees between height and the cone side.
11. Regular hexagonal pyramid Calculate the height of a regular hexagonal pyramid with a base edge of 5 cm and a wall height of w = 20cm. Sketch a picture.
12. Tetrahedral pyramid Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30´.
13. Hexagonal pyramid Please calculate the height of a regular hexagonal pyramid with a base edge of 5cm and a wall height of w = 20cm. Please sketch a picture.
14. The aspect ratio The aspect ratio of the rectangular triangle is 13: 12: 5. Calculate the internal angles of the triangle.
15. Eq triangle minus arcs In an equilateral triangle with a 2cm side, the arcs of three circles are drawn from the centers at the vertices and radii 1cm. Calculate the content of the shaded part - a formation that makes up the difference between the triangle area and circular cuts
16. Hexagon Calculate the surface of a regular hexagonal prism whose base edge a = 12cm and side edge b = 3 dm.
17. Three parallels The vertices of an equilateral triangle lie on 3 different parallel lines. The middle line is 5 m and 3 m distant from the end lines. Calculate the height of this triangle.
18. The hemisphere The hemisphere container is filled with water. What is the radius of the container when 10 liters of water pour from it when tilted 30 degrees?
19. Medians in right triangle It is given a right triangle, angle C is 90 degrees. I know it medians t1 = 8 cm and median t2 = 12 cm. .. How to calculate the length of the sides?
20. Rectangular trapezoid In a rectangular trapezoid ABCD with right angles at vertices A and D with sides a = 12cm, b = 13cm, c = 7cm. Find the angles beta and gamma and height v.

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Pythagorean theorem is the base for the right triangle calculator.