# Angle + length - examples

- The mast

The top of the pole we see at an angle of 45°. If we approach the pole by 10 m, we see the top of the pole at an angle of 60°. What is the height of the pole? - 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 Dunaj average falls, if on section long 957 km flowing water from 1454 m AMSL to 101 m AMSL. - Clock

How many times a day hands on a clock overlap? - 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. - Observer

The observer sees straight fence 100 m long in 30° view angle. From one end of the fence is 153 m. How far is it from the another end of the fence? - IS triangle

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

Calculate the average slope (in promiles and even in degrees) of the rail tracks between Prievidza (309 m AMSL) and Nitra (167 m AMSL), if the track is 77 km long. - 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°. - Earth parallel

Earth's radius is 6375 km long. Calculate the length parallel of latitude 10°. - Climb in percentage

The height difference between points A and B is 587 m. Calculate the percentage of route climbing if the horizontal distance places A, B is 4.8 km. - Diagonal

Determine the dimensions of the cuboid, if diagonal long 31 dm has angle with one edge 61° and with other edge 52°. - Quarter circular

The wire that is hooked around the perimeter of quarter-circular arc has length 3π+12. Determine the radius of circle arc. - Angles

Determine the interior angles of a rhombus with area 319.1 cm^{2}and perimeter 72 cm. - Gear wheels

Two gear wheels, which fit together have number of teeth z_{1}=72 and z_{2}=200. Calculate the speed of the first wheel, if the second wheel rotates 503 revolutions per minute. - Tower

How many m^{2}of copper plate should be to replace roof of the tower conical shape with diameter 24 m and the angle at the vertex of the axial section is 144°? - Cuboid

Determine the dimensions of cuboid a, b, c; if diagonal d=9 dm has angle with edge a α=55° and has angle with edge b β=58° - Clocks

How long path will walk the end of the clock's minute-hand long 7 cm for 330 minutes? How long will walk in the same time hour-hand? - Building

How high is the building that throws horizontal shadow 95.4 m long at angle 50°? - Track arc

Two straight tracks is in an angle 74°. They will join with circular arc with radius r=1127 m. How long will be arc connecting these lines (L)? How far is the center point of arc from track crossings (x)?

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