Right triangle - math word problems - page 7

1. Hexagonal pyramid Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length 3 cm and a height 5 cm.
2. Height Is right that in any right triangle height is less or equal half of the hypotenuse?
3. n-gon What is the side length of the regular 5-gon inscribed in a circle of radius 12 cm?
4. Right triangle Calculate the missing side b and interior angles, perimeter and area of ​​a right triangle if a=10 cm and hypotenuse c = 16 cm.
5. Two forces Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.
6. Rhombus Internal angles of rhombus is in ratio 2:3. How many times is the shorter diagonal longer than side of rhombus? An airplane leaves an airport and flies due west 120 miles and then 150 miles in the direction S 44.1°W. How far is the plane from the airport (round to the nearest mile)?
8. Track arc Two straight tracks is in an angle 74°. They will join with circular arc with radius r=1127 m. How long will be arc connecting these lines (L)? How far is the center point of arc from track crossings (x)?
9. Perimeter and legs Determine the perimeter of a right triangle if the length of one leg is 75% length of the second leg and its content area is 24 cm2.
10. Prism The lenght, width and height of a right prism are 6, 17 and 10 respectively. What is the lenght of the longest segment whose endpoints are vertices of the prism?
11. House roof The roof of the house has the shape of a regular quadrangular pyramid with a base edge 17 m. How many m2 is needed to cover roof if roof pitch is 57° and we calculate 11% of waste, connections and overlapping of area roof?
12. V-belt Calculate the length of the belt on pulleys with diameters of 105 mm and 393 mm at shaft distance 697 mm.
13. Pentagonal pyramid Calculate the volume of a regular 5-side (pentaprism) pyramid ABCDEV; if |AB| = 7.7 cm and a plane ABV, ABC has angle 37 degrees.
14. Two balls Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them.
15. Arm Calculate the length of the arm r of isosceles triangle ABC, with base |AB| = 18 cm and a height v=17 cm.
16. Cone and the ratio Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface.
17. EQL triangle Calculate inradius and circumradius of equilateral triangle with side a=77 cm.
18. Block Calculate the volume of a cuboid ABCDEFGH if |AB| = 16 cm, |BC| = 19 cm and the angle ∠CDG = 36.9°
19. Vector Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2).
20. Euklid4 Legs of a right triangle have dimensions 244 m and 246 m. Calculate the length of the hypotenuse and the height of this right triangle.

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