Angle - 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?
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.
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.
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: ? ?
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 dm2. Calculate the volume of a cone.
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.
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?
Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ?
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.
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 climb 7.4 ‰. Calculate the height difference between two points on the railway distant 3539 meters.