Angle - 9th grade (14y) - examples
Calculate how many promiles river Vltava average falls, if on section long 695 km flowing water from 1601 m AMSL to 183 m AMSL.
- Trigonometric functions
In right triangle is: ? Determine the value of s and c: ? ?
How many times a day hands on a clock overlap?
From the observatory 18 m high and 26 m from the river bank, river width appears in the visual angle φ = 14°30'. Calculate width of the river.
- 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.
Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ?
- IS triangle
Calculate interior angles of the isosceles triangle with base 37 cm and legs 36 cm long.
- Cuboid diagonal
Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 7:10:8 and if you know that the wall diagonal AC is 21 cm and angle between AC and the body diagonal AG is 40 degrees.
- Slope of track
Calculate the average slope of the rail tracks between Prievidza (309 m AMSL) and Bratislava (152 m AMSL), if the track is 158 km long.
Calculate volume and surface area of the cone with diameter of the base d = 12 cm and side of cone with the base has angle 41°47'59″.
Mast has 9 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 9.8°. Determine the height of the mast, if the sun above the horizon is at angle 36°6'.
- Isosceles right triangle
Calculate the area of an isosceles right triangle whose perimeter is 236 dm.
Calculate the length of the side FL and diagonal JL of rectangle JFLB when given: |BL| = 33 cm and angle ∠ JFB = 32 degrees.
Railways climb 5.8 ‰. Calculate the height difference between two points on the railway distant 2389 meters.
Convert 54° to radians. Write result as multiple of number π.
Determine the dimensions of the cuboid, if diagonal long 16 dm has angle with one edge 66° and with other edge 71°.
- Circular pool
The base of pool is circle with a radius r = 10 m excluding circular segment that determines chord length 10 meters. Pool depth is h = 2m. How many hectoliters of water can fit into the pool?
Determine the interior angles of a rhombus with area 240.6 cm2 and perimeter 64 cm.
- Rotation of the Earth
Calculate the circumferential speed of the Earth's surface at a latitude of 53.7°. Consider a globe with a radius of 6378 km.
- Arc and segment
Calculate the length of circular arc l, area of the circular arc S1 and area of circular segment S2. Radius of the circle is 49 and corresponding angle is ?.