# Angle - examples

- A cylinder

A cylinder 108 cm high has a circumference of 24 cm. A string makes exactly 6 complete turns around the cylinder while its two ends touch the cylinder's top and bottom. (forming a spiral around the cylinder). How long is the string in cm? - 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 - Largest angle of the triangle

Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a - Rhombus 29

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

The three points A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB and DC is parallel to AB. Calculate the coordinates of D. - 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. - 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: ?

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