# High school + right triangle - examples

1. The diagram 2
The diagram shows a cone with slant height 10.5cm. If the curved surface area of the cone is 115.5 cm2. Calculate correct to 3 significant figures: *Base Radius *Height *Volume of the cone
2. Find parameters
Find parameters of the circle in the plane - coordinates of center and radius: ?
3. Lighthouse
Marcel (point J) lies in the grass and sees the top of the tent (point T) and behind it the top of the lighthouse (P). | TT '| = 1.2m, | PP '| = 36m, | JT '| = 5m. Marcel lies 15 meters away from the sea (M). Calculate the lighthouse distance from the sea.
4. Isosceles triangle 8
If the rate of the sides an isosceles triangle is 7:6:7, find the base angle correct to the nearest degree.
5. Cable car
Find the elevation difference of the cable car when it rises by 67 per mille and the rope length is 930 m.
6. Spherical cap 4
What is the surface area of a spherical cap, the base diameter 20 m, height 2.5 m? Calculate using formula.
7. 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.
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. River
Calculate how many promiles river Dunaj average falls, if on section long 957 km flowing water from 1454 m AMSL to 101 m AMSL.
12. Trigonometric functions
In right triangle is: ? Determine the value of s and c: ? ?
13. Cuboid
Cuboid with edge a=16 cm and body diagonal u=45 cm has volume V=11840 cm3. Calculate the length of the other edges.
14. Tetrahedral pyramid
What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=7 and height v=6?
15. 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°.
16. Square
Points A[-5,-6] and B[7,-1] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD.
17. Cubes
One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm2.
18. Cone A2V
Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
19. 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
20. 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.

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