# Pythagorean theorem - problems - page 11

1. TV diagonal
Diagonal TV is 0.56 m long, how big the television sreen is if the aspect ratio is 16:9?
5.2 meters long ladder is leaning against the wall of the well and its lower end is 1.3 meters from this wall. How high from the bottom of a well is the top edge of the ladder?
3. Pyramid 8
Calculate the volume and the surface area of a regular quadrangular pyramid with the base side 9 cm and side wall with the base has an angle 75°.
4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall?
5. 3sides prism
The base of vertical prism is an isosceles triangle whose base is 10 cm and the arm is 13 cm long. Prism height is three times the height of base triangle. Calculate the surface area of the prism.
6. Circles
In the circle with a radius 7.5 cm are constructed two parallel chord whose lengths are 9 cm and 12 cm. Calculate the distance of these chords (if there are two possible solutions write both).
7. Euclidean distance
Calculate the Euclidean distance between shops A, B and C, where: A 45 0.05 B 60 0.05 C 52 0.09 Wherein the first figure is the weight in grams of bread and second figure is price in USD.
8. Cube wall
Calculate the cube's diagonal diagonal if you know that the surface of one wall is equal to 36 centimeters square. Please also calculate its volume.
9. Euclid 5
Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm.
10. 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
11. Logs
The log has diameter 30 cm. What's largest beam with a rectangular cross-section can carve from it?
12. 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.
13. Distance
Wha is the distance between the origin and the point (18; 22)?
14. 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?
15. Square2
Side of the square is a = 6.2 cm, how long is its diagonal?
16. Height UT
How long is height in the equilateral triangle with a side b = 43?
17. Acreage
What acreage has a rectangular plot whose diagonal is 34 meters long and one side has a length of 16 meters. ?
18. 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?
19. 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.
20. 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?

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Pythagorean theorem is the base for the right triangle calculator.