# Right triangle - math word problems

1. Column
Perpendicular pole high 8 m tall broke and its toe fell 2.7 m from the bottom of the pole. At what height above the ground pole broke?
2. Right angled
From the right triangle with legs 12 cm and 20 cm we built a square with the same content as the triangle. How long will be side of the square?
3. Rhombus
Calculate the length of the diagonal AC of the rhombus ABCD, if its perimeter is 84 dm and the other diagonal BD has length 20 dm.
4. Hexagon
There is regular hexagon ABCDEF. If area of the triangle ABC is 22, what is area of the hexagon ABCDEF? I do not know how to solve it simply....
5. Leg and height
Solve right triangle with height v = 9.6 m and shorter cathetus b = 17.3 m.
6. Isosceles III
The base of the isosceles triangle is 17 cm area 416 cm2. Calculate the perimeter of this triangle.
7. Without Euclid laws
Right triangle ABC with right angle at the C has a=5 and hypotenuse c=19. Calculate the height h of this triangle without the use of Euclidean laws.
8. XY triangle
Determine area of triangle given by line 7x+8y-69=0 and coordinate axes x and y.
9. Pyramid
Pyramid has a base a = 5cm and height in v = 8 cm. a) calculate angle between plane ABV and base plane b) calculate angle between opposite side edges.
10. Isosceles triangle
What are the angles of an isosceles triangle ABC if its base is long a=5 m and has an arm b=4 m.
11. Cut and cone
Calculate the volume of the rotation cone which lateral surface is circle arc with radius 15 cm and central angle 63 degrees.
12. Rotary cone
The volume of the rotation of the cone is 472 cm3 and angle between the side of the cone and base angle is 70°. Calculate lateral surface area of this cone.
13. Diagonals
Rhombus has two diagonals e=14 dm and f=11 dm. Calculate the side angle and height of the rhombus.
14. Oil rig
Oil drilling rig is 23 meters height and fix the ropes which ends are 7 meters away from the foot of the tower. How long are these ropes?
15. Boat
A force of 300 kg (3000 N) is required to pull a boat up a ramp inclined at 14° with horizontal. How much does the boat weight?
16. Maple
Maple peak is visible from a distance 3 m from the trunk from a height of 1.8 m at angle 62°. Determine the height of the maple.
17. n-gon II
What is the side length of the regular 5-gon circumscribed circle of radius 11 cm?
18. n-gon
What is the side length of the regular 5-gon inscribed in a circle of radius 12 cm?
19. Canopy
Mr Peter has metal roof cone shape with a height of 127 cm and radius 130 cm over well. He needs paint the roof with anticorrosion. How many kg of color must he buy if the manufacturer specifies the consumption of 1 kg to 3.3 m2?
20. Block
Calculate the volume of a cuboid ABCDEFGH if |AB| = 16 cm, |BC| = 19 cm and the angle ∠CDG = 36.9°

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