# Angle - 8th grade (13y) - examples

- Circular arc

Calculate the length of the circular arc if the diameter d = 20cm and the angle alpha = 142 ° - 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? - A boy

A boy of height 1.7m is standing 30m away from flag staff on the same level ground . He observes that the angle of deviation of the top of flag staff is 30 degree. Calculate the height of flag staff. - 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? - Right angled triangle 3

Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees - Rhombus 29

One of the diagonals of a rhombus is equal to a side of the rhombus. Find the angles of the rhombus. - Complementary angles 2

Two complementary angles are (x+4) and (2x - 7) find the value of x - Ruler and compass

Use a ruler and compass to construct a triangle ABC with AB 5cm BAC 60° and ACB 45°. - Hands

The clock shows 12 hours. After how many minutes will agle between hour and minute hand 90°? Consider the continuous movement of both hands hours. - River

Calculate how many promiles river Vltava average falls, if on section long 928 km flowing water from 1592 m AMSL to 108 m AMSL. - Clock

How many times a day hands on a clock overlap? - Is right?

Is triangle with sides 51, 56 and 77 right triangle? - Cone A2V

Surface of cone in the plane is a circular arc with central angle of 126° and area 415 dm^{2.}Calculate the volume of a cone. - 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. - IS triangle

Calculate interior angles of the isosceles triangle with base 38 cm and legs 26 cm long. - Cuboid diagonal

Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 9:3:8 and if you know that the wall diagonal AC is 86 cm and angle between AC and the body diagonal AG is 25 degrees. - Slope of track

Calculate the average slope of the rail tracks between Prievidza (309 m AMSL) and Topoľčany (174 m AMSL), if the track is 44 km long. - Cone

Calculate volume and surface area of the cone with diameter of the base d = 19 cm and side of cone with the base has angle 48°36'. - Mast

Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 15°. Determine the height of the mast, if the sun above the horizon is at angle 33°. - Railways

Railways climb 7.4 ‰. Calculate the height difference between two points on the railway distant 3539 meters.

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