Triangle - 9th grade (14y) - examples

1. Rectangular trapezoid In a rectangular trapezoid ABCD with right angles at vertices A and D with sides a = 12cm, b = 13cm, c = 7cm. Find the angles beta and gamma and height v.
2. RT sides Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm.
3. Height of the room Given the floor area of a room as 24 feet by 48 feet and space diagonal of a room as 56 feet. Can you find the height of the room?
4. Perimeter of RT Find the circumference of the rectangular triangle if the sum of its legs is 22.5 cm and its area is 62.5 cm2.
5. Pyramid height Find the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height h = 20cm.
6. Trapezoid MO The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
7. Garden Area of a square garden is 6/4 of triangle garden with sides 56 m, 35 m, and 35 m. How many meters of fencing need to fence a square garden?
8. Right Δ A right triangle has the length of one leg 28 cm and length of the hypotenuse 53 cm. Calculate the height of the triangle.
9. Axial section Axial section of the cone is an equilateral triangle with area 208 dm2. Calculate the volume of the cone.
10. Circle chord What is the length d of the chord circle of diameter 36 m, if the distance from the center circle is 16 m?
11. Rectangle The rectangle is 11 cm long and 45 cm wide. Determine the radius of the circle circumscribing rectangle.
12. Trigonometric functions In right triangle is: ? Determine the value of s and c: ? ?
13. Tetrahedral pyramid What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=7 and height v=6?
14. Triangle SAS Calculate the area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °.
15. Short cut Imagine that you are going to the friend. That path has a length 330 meters. Then turn left and go another 2000 meters and you are at a friend's. The question is how much the journey will be shorter if you go direct across the field?
16. Gimli Glider Aircraft Boeing 767 lose both engines at 42000 feet. The plane captain maintain optimum gliding conditions. Every minute, lose 1910 feet and maintain constant speed 211 knots. Calculate how long takes to plane from engines failure to hit ground. Calculate
17. River From the observatory 11 m high and 24 m from the river bank, river width appears in the visual angle φ = 13°. Calculate width of the river.
18. Regular 5-gon Calculate area of the regular pentagon with side 7 cm.
19. Right triangle Alef The obvod of a right triangle is 84 cm, the hypotenuse is 37 cm long. Determine the lengths of the legs.
20. Rectangle In rectangle with sides, 10 and 8 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle?

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