Right triangle - 9th grade (14y) - math problems

  1. Cosine
    cosine The point (8, 6) is on the terminal side of angle θ. cos θ = ?
  2. Quadrilateral
    diamond_2 In the square ABCD point P is in the middle of the DC side and point Q in the middle pages AD. If the area of quadrilateral BQPC is 49 cm2, what is the area of ABCD?
  3. Cone and the ratio
    kuzel 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.
  4. Sails
    ship_nina We known heights 220, 165 and 132 of sail. It has triangular shape. What is the surface of the sail?
  5. RT 11
    right_triangle Calculate the area of right tirangle if its perimeter is p = 45 m and one cathethus is 20 m long.
  6. Distance
    origin_math Wha is the distance between the origin and the point (18; 22)?
  7. Leg
    tetris Determine the area of a trapezoid with bases 71 and 42 and height is 4 shorter than the its leg.
  8. Cosine
    theta Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 3 and 8 and with the hypotenuse 8.544.
  9. Inscribed rectangle
    circle_desc_rectangular The circle area is 216. Determine the area of inscribed rectangle with one side 5 long.
  10. ISO trapezium
    trapezium_2 Calculate area of isosceles trapezoid with base 95 long, leg 27 long and with the angle between the base and leg 70 degrees.
  11. 30-60-90
    30-60-90 The longer leg of a 30°-60°-90° triangle measures 5. What is the length of the shorter leg?
  12. Chord - TS
    chord_TS The radius of circle k measures 68 cm. Arc GH = 47 cm. What is TS?
  13. EQL triangle
    rs_triangle Calculate inradius and circumradius of equilateral triangle with side a=77 cm.
  14. Flowerbed
    triangle_flowers.JPG Flowerbed has the shape of an isosceles obtuse triangle. Arm has a size 5.5 meters and an angle opposite to the base size is 94°. What is the distance from the base to opposite vertex?
  15. Semicircle
    tales-de-mileto In the semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC?
  16. Cable car 2
    lanovka_1 Cable car rises at an angle 41° and connects the upper and lower station with an altitude difference of 1175 m. How long is the track of cable car?
  17. Circle section
    circle_segment Equilateral triangle with side 33 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector
  18. Trapezoid ABCD
    trapezoid_2 Calculate the perimeter of trapezoid ABCD if we know the side c=15, b=19 which is also a height and side d=20.
  19. Hexagon A
    hexagon Calculate area of regular hexagon inscribed in circle with radius r=9 cm.
  20. Tower
    HexagonalPyramid_4 The top of the tower is a regular hexagonal pyramid with base edge 8 meters long and a height 5 meters. How many m2 of the sheet is required to cover the top of the tower if we count 8% of the sheet waste?

Do you have an interesting mathematical word problem that you can't solve it? Enter it, and we can try to solve it.



We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...



See also our right triangle calculator.