# Right triangle - math word problems

1. Sides of right angled triangle One leg is 1 m shorter than the hypotenuse, and the second leg is 2 m shorter than the hypotenuse. Find the lengths of all sides of the right-angled triangle.
2. Coordinates of square vertices I have coordinates of square vertices A / -3; 1/and B/1; 4 /. Find coordinates of vertices C and D, C 'and D'. Thanks Peter.
3. A rhombus A rhombus has sides of length 10 cm, and the angle between two adjacent sides is 76 degrees. Find the length of the longer diagonal of the rhombus.
4. Isosceles triangle 10 In an isosceles triangle, the equal sides are 2/3 of the length of the base. Determine the measure of the base angles.
5. 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?
6. A concrete pedestal A concrete pedestal has a shape of a right circular cone having a height of 2.5 feet. The diameter of the upper and lower bases are 3 feet and 5 feet, respectively. Determine the lateral surface area, total surface area, and the volume of the pedestal.
7. Cuboid face diagonals The lengths of the cuboid edges are in the ratio 1: 2: 3. Will the lengths of its diagonals be the same ratio? The cuboid has dimensions of 5 cm, 10 cm, and 15 cm. Calculate the size of the wall diagonals of this cuboid.
8. Body diagonal Calculate the volume of a cuboid whose body diagonal u is equal to 6.1 cm. Rectangular base has dimensions of 3.2 cm and 2.4 cm
9. Uphill garden I have a garden uphill, increasing from 0 to 4.5 m for a length of 25 m, how much is the climb in percent?
10. Hole's angles I am trying to find an angle. The top of the hole is .625” and the bottom of the hole is .532”. The hole depth is .250” what is the angle of the hole (and what is the formula)?
11. Secret treasure Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure.
12. The plaster cast The plaster cast has the shape of a regular quadrilateral pyramid. The cover consists of four equilateral triangles with a 5 m side. Calculate its volume and surface area.
13. 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?
14. Faces diagonals If the diagonals of a cuboid are x, y, and z (wall diagonals or three faces) respectively than find the volume of a cuboid. Solve for x=1.2, y=1.7, z=1.45
15. Wall and body diagonals Calculate the lengths of the wall and body diagonals of the cuboid with edge dimensions of 0.5 m, 1 m, and 2 m
16. Tetrahedral pyramid A regular tetrahedral pyramid is given. Base edge length a = 6.5 cm, side edge s = 7.5 cm. Calculate the volume and the area of its face (side area).
17. Two chords Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle.
18. Angles of elevation From points A and B on level ground, the angles of elevation of the top of a building are 25° and 37° respectively. If |AB| = 57m, calculate, to the nearest meter, the distances of the top of the building from A and B if they are both on the same side of t
19. Space diagonal The space diagonal of a cube is 129.91 mm. Find the lateral area, surface area and the volume of the cube.
20. The Eiffel Tower The top of the Eiffel Tower is seen from a distance of 600 meters at an angle of 30 degrees. Find the tower height.

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