# Right triangle - problems - page 26

1. Is right-angled
Can a triangle with the sides of sqrt 3, sqrt 5 and sqrt 8 (√3, √5 a √8) be a right triangle?
2. 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?
3. Find the 5
Find the equation with center at (1,20) which touches the line 8x+5y-19=0
4. 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?
5. 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
6. 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?
7. 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?
8. Vector 7
Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|.
9. Decagon
Calculate the area and circumference of the regular decagon when its radius of a circle circumscribing is R = 1m
10. Two people
Two straight lines cross at right angles. Two people start simultaneously at the point of intersection. John walking at the rate of 4 kph in one road, Jenelyn walking at the rate of 8 kph in the other road. How long will it take for them to be 20√5 km apar
11. Sphere equation
Obtain the equation of sphere its centre on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1).
12. Isosceles
Isosceles trapezium ABCD ABC = 12 angle ABC = 40 ° b=6. Calculate the circumference and area.
13. 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?
14. Ratio of edges
The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid.
15. 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.
16. Quarter circle
What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm?
17. 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?
18. Equilateral triangle
A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side.
19. Rectangular trapezoid
The ABCD rectangular trapezoid with the AB and CD bases is divided by the diagonal AC into two equilateral rectangular triangles. The length of the diagonal AC is 62cm. Calculate trapezium area in cm square and calculate how many differs perimeters of the.
20. The perimeter
The perimeter of equilateral △PQR is 12. The perimeter of regular hexagon STUVWX is also 12. What is the ratio of the area of △PQR to the area of STUVWX?

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