# Angle - problems

- 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? - Construct

Construct a triangle ABC inscribed circle has a radius r = 2 cm, the angle alpha = 50 degrees = 8 cm. Make a sketch, analysis, construction and description. - Diagonals of pentagon

Calculate the diagonal length of the regular pentagon: a) inscribed in a circle of radius 12dm; b) a circumscribed circle with a radius of 12dm. - Supplementary angles

One of the supplementary angles is larger by 33° than the second one. Calculate the angles size. - 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. - Trigonometric functions

In right triangle is: ? Determine the value of s and c: ? ? - 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. - 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? - It is rectangular?

Size of two of the angles in a triangle are: α=110°, β=40°. Is it a right triangle? - Right

Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ? - Triangle

Triangle KLM is given by plane coordinates of vertices: K[-12, -11] L[-15, -18] M[-13, -12]. Calculate its area and itsinterior angles. - 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 (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. - Cone

Calculate volume and surface area of the cone with diameter of the base d = 15 cm and side of cone with the base has angle 52°. - Railways

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

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