# Triangle - examples - page 23

1. Equation of circle 2 Find the equation of a circle which touches the axis of y at a distance 4 from the origin and cuts off an intercept of length 6 on the axis x.
2. Lighthouse The man, 180 cm tall, walks along the seafront directly to the lighthouse. The male shadow caused by the beacon light is initially 5.4 meters long. When the man approaches the lighthouse by 90 meters, its shadow shorter by 3 meters. How tall is the lightho
3. A bridge A bridge over a river is in the shape of the arc of a circle with each base of the bridge at the river's edge. At the center of the river, the bridge is 10 feet above the water. At 27 feet from the edge of the river, the bridge is 9 feet above the water. H
4. Road The angle of a straight road is approximately 12 degrees. Determine the percentage of this road.
5. Two forces The two forces F1 = 580N and F2 = 630N have the angle of 59 degrees. Calculate their resultant force F.
6. Clouds Approximately at what height is the cloud we see under an angle of 26°10' and see the Sun at an angle of 29°15' and the shade of the cloud is 92 meters away from us?
7. Ratio of sides The triangle has a circumference of 21 cm and the length of its sides is in a ratio of 6: 5: 3. Find the length of the longest side of the triangle in cm.
8. Prove Prove that k1 and k2 is the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x2+y2+2x+4y+1=0 k2: x2+y2-8x+6y+9=0
9. Diagonals at right angle In the trapezoid ABCD this is given: AB=12cm CD=4cm And diagonals crossed under a right angle. What is the area of this trapezoid ABCD?
10. Garden fence The garden has the shape of a rectangular triangle with an area of 96 square meters and a 16 m long one leg. How many meters of the fence need to be fenced?
11. Thales Thales is 1 m from the hole. The eyes are 150 cm above the ground and look into the hole with a diameter of 120 cm as shown. Calculate the depth of the hole.
12. Display case Place a glass shelf at the height of 1m from the bottom of the display case in the cabinet. How long platter will we place at this height? The display case is a rectangular triangle with 2 m and 2.5 m legs.
13. Shadow of tree Miro stands under a tree and watching its shadow and shadow of the tree. Miro is 180 cm tall and its shade is 1.5 m long. The shadow of the tree is three times as long as Miro's shadow. How tall is the tree in meters?
14. Decagon Calculate the area and circumference of the regular decagon when its radius of a circle circumscribing is R = 1m
15. Triangular prism Calculate the volume of a triangular prism 10 cm high, the base of which is an equilateral triangle with dimensions a = 5 cm and height va = 4,3 cm
16. Regular quadrangular pyramid The height of the regular quadrangular pyramid is 6 cm, the length of the base is 4 cm. What is the angle between the ABV and BCV planes?
17. Isosceles Isosceles trapezium ABCD ABC = 12 angle ABC = 40 ° b=6. Calculate the circumference and area.
18. Angle of diagonal Angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10cm. Calculate the body volume.
19. ABCD square In the ABCD square, the X point lies on the diagonal AC. The length of the XC is three times the length of the AX segment. Point S is the center of the AB side. The length of the AB side is 1 cm. What is the length of the XS segment?
20. Equilateral triangle A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side.

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