# Pythagorean theorem - problems - page 12

1. Triangular pyramid
Determine the volume and surface area of a regular triangular pyramid having a base edge a=20 cm and a lateral edge b = 35 cm
2. Euclid 5
Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm.
3. Logs
The log has diameter 30 cm. What's largest beam with a rectangular cross-section can carve from it?
4. Rhombus IV
Calculate the length of the diagonals of the rhombus, whose lengths are in the ratio 1: 2 and a rhombus side is 35 cm.
5. Distance
Wha is the distance between the origin and the point (18; 22)?
6. Journey
Charles and Eva stands in front of his house, Charles went to school south at speed 5.4 km/h, Eva went to the store on a bicycle eastwards at speed 21.6 km/h. How far apart they are after 10 minutes?
7. Height UT
How long is height in the equilateral triangle with a side b = 43?
8. Church roof
The roof of the church tower has the shape of a regular tetrahedral pyramid with base edge length 5.4 meters and a height 5 m. It was found that needs to be corrected 27% covering of the roof area. What amount of material will be required?
9. Square2
Side of the square is a = 6.2 cm, how long is its diagonal?
A ship travels 84 km on a bearing of 17°, and then travels on a bearing of 107° for 135 km. Find the distance of the end of the trip from the starting point, to the nearest kilometer.
11. Acreage
What acreage has a rectangular plot whose diagonal is 34 meters long and one side has a length of 16 meters. ?
12. Tetrahedral pyramid
It is given a regular tetrahedral pyramid with base edge 6 cm and the height of the pyramid 10 cm. Calculate the length of its side edges.
13. Isosceles IV
In an isosceles triangle ABC is |AC| = |BC| = 13 and |AB| = 10. Calculate the radius of the inscribed (r) and described (R) circle.
14. Round table
Round table with diameter d = 105 cm is coated by square tablecloth with a side length 121 cm. About how many cm is higher center of tablecloth than its cornes?
15. 3d vector component
The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3?
16. Square
Rectangular square has side lengths 183 and 244 meters. How many meters will measure the path that leads straight diagonally from one corner to the other?
17. Sphere vs cube
How many % of the surface of a sphere of radius 12 cm is the surface of a cube inscribed in this sphere?
18. Concentric circles
In the circle with diameter 19 cm is constructed chord 9 cm long. Calculate the radius of a concentric circle that touches this chord.
19. Diagonal 20
Diagonal pathway for the rectangular town plaza whose length is 20 m longer than the width. if the pathway is 20 m shorter than twice the width. How long should the pathway be?
20. RT leg and perimeter
Calculate the length of the sides of a right triangle ABC with hypotenuse c when the length of a leg a= 84 and perimeter of the triangle o = 269.

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Pythagorean theorem is the base for the right triangle calculator.