# Triangle + Pythagorean theorem - examples

1. 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.
2. Find parameters
Find parameters of the circle in the plane - coordinates of center and radius: ?
3. Cable car
Find the elevation difference of the cable car when it rises by 67 per mille and the rope length is 930 m.
4. Cincinnati
A map is placed on a coordinate grid. Cincinnati located at (5,4) and San Diego is located at (-10, -3). How far apart is Cincinnati from San Diego on the map? Round to the nearest tenth.
5. 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.
6. Garden
Area of 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?
7. Right Δ
Right triangle has length of one leg 28 cm and length of the hypotenuse 53 cm. Calculate the height of the triangle.
8. Axial section
Axial section of the cone is equilateral triangle with area 208 dm2. Calculate volume of the cone.
9. Circle chord
What is the length d of the chord circle of diameter 36 m, if distance from the center circle is 16 m?
10. Rectangle
The rectangle is 11 cm long and 45 cm wide. Determine the radius of the circle circumscribing rectangle.
11. Trigonometric functions
In right triangle is: ? Determine the value of s and c: ? ?
12. Tetrahedral pyramid
What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=7 and height v=6?
13. Triangle SAS
Calculate area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130°.
14. Is right?
Is triangle with sides 51, 56 and 77 right triangle?
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 14 m high and 32 m from the river bank, river width appears in the visual angle φ = 20°. Calculate width of the river.
18. 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?
19. Square and circles
Square with sides 61 mm is circumscribed and inscribed with circles. Determine the radiuses of both circles.
20. Rhombus ABCD
Rhombus ABCD, |AC| = 90 cm, |BD| = 49 cm. Calculate the perimeter of the rhombus ABCD.

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