Right triangle - math word problems - page 27

1. Coordinate axes Determine the area of the triangle given by line -7x+7y+63=0 and coordinate axes x and y.
2. Sphere from tree points Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a Given is a regular quadrangular pyramid with a square base. The body height is 30 cm and volume V = 1000 cm³. Calculate its side a and its surface area.
4. Diagonal to area Calculate the area of a rectangle in which the length of the diagonal is 10 cm.
5. Find diagonal Find diagonal of cuboid with length=20m width=25m height=150m
6. Ellipse Ellipse is expressed by equation 9x2 + 25y2 - 54x - 100y - 44 = 0. Find the length of primary and secondary axes, eccentricity, and coordinates of the center of the ellipse.
7. The pond We can see the pond at an angle 65°37'. Its end points are 155 m and 177 m away from the observer. What is the width of the pond?
8. The sides 2 The sides of a trapezoid are in the ratio 2:5:8:5. The trapezoid’s area is 245. Find the height and the perimeter of the trapezoid.
9. Diamond diagonals Find the diamond diagonal's lengths if the area is 156 cm2 and side is 13 cm long.
10. Nonagon Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm
11. Right triangle Calculate the length of the remaining two sides and the angles in the rectangular triangle ABC if a = 10 cm, angle alpha = 18°40'.
12. Body diagonal Calculate the length of the body diagonal of the 6cm cube.
13. Is right triangle or not If right triangle ABC, have sides a=13, b=11.5, c=22.5. Find area.
14. Cube diagonals The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal. Find radius of circle using pythagorean theorem where a=9, b=r, c= 6+r
16. Three points 2 The three points A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB and DC is parallel to AB. Calculate the coordinates of D.
17. Diagonals of a rhombus 2 One diagonal of a rhombus is greater than other by 4 cm . If the area of the rhombus is 96 cm2, find the side of the rhombus.
18. Construct Construct a rhombus ABCD, if the size of the diagonal AC is 6 cm and diagonal BD 8 cm long.
19. Cone 15 The radius of the base of a right circular cone is 14 inches and it's height 18 inches. What is the slant height?
20. Cuboidal room Length of cuboidal room is 2m breadth of cuboidal room is 3m and height is 6m find the length of the longest rod that can be fitted in the room

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