# Right triangle - math word problems

1. 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.
2. XY triangle Determine area of triangle given by line 7x+8y-69=0 and coordinate axes x and y.
3. 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.
4. 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.
5. 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.
6. Diagonals Rhombus has two diagonals e=14 dm and f=11 dm. Calculate the side angle and height of the rhombus.
7. 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.
8. 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?
9. 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?
10. 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.
11. 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?
12. n-gon II What is the side length of the regular 5-gon circumscribed circle of radius 11 cm?
13. n-gon What is the side length of the regular 5-gon inscribed in a circle of radius 12 cm?
14. Block Calculate the volume of a cuboid ABCDEFGH if |AB| = 16 cm, |BC| = 19 cm and the angle ∠CDG = 36.9°
15. Cone Calculate volume and surface area of ​​the cone with a diameter of the base d = 15 cm and side of cone with the base has angle 52°.
16. Tower How many m2 of copper plate should be to replace roof of the tower conical shape with diameter 24 m and the angle at the vertex of the axial section is 144°?
17. Diagonal Calculate the length of the diagonal of the rectangle ABCD with sides a = 8 cm, b = 7 cm.
18. Arm Calculate the length of the arm r of isosceles triangle ABC, with base |AB| = 14 cm and a height v=18 cm.
19. Thales Calculate the length of the Thales' circle described to right triangle with hypotenuse 18.4 cm.
20. Base Compute base of an isosceles triangle, with the arm a=20 cm and a height above the base h=10 cm.

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