Angle - problems
- Isosceles right triangle
Calculate the area of an isosceles right triangle whose perimeter is 236 dm.
Rhombus-shaped jewel have area of 86 mm2 and the edge in long 10 mm. Calculate the size of rhombus acute angle.
- n-gon II
What is the side length of the regular 9-gon circumscribed circle of radius 13 cm?
- Side c
In △ABC a=3, b=8 and ∠C=70°. Calculate length of the side c.
- Minute angle
Determine size of angle, which takes minute hand for 90 minutes.
- Glass of juice
Glass of juice shaped cylinder 16 cm height and base diameter of 10 cm is filled with juice so that the level is 3 cm below the rim of the glass. Determine the maximum angle of the cup can be tilted and juice don't overflow.
The perimeter of a circular sector with an angle 2 rad is 53 cm. Determine the radius of the circle from which the sector comes.
The plane flies at altitude 6800 m. At the time of first measurement was to see the elevation angle of 20° and second measurement of the elevation angle of 34°. Calculate the distance the plane flew between the two measurements.
For horizontal distance 3 km road rise by 5.4 m. Calculate the road pitch in ‰ (permille, parts per thousand).
- Angles of the triangle
ABC is a triangle. The size of the angles alpha, beta are in a ratio 4: 7. The angle gamma is greater than the angle alpha by a quarter of a straight angle. Determine angles of the triangle ABC.
- Circle sector
Circular sector with a central angle 10 ° has area 254 cm2. Calculate its radius r.
The outer angle of the triangle ABC at the vertex A is 121°5'59″. The outer angle at the vertex B is 137°18'. What size is the internal angle at the vertex C?
The point (21, 20) is on the terminal side of angle θ. cos θ = ?
- Smallest internal angle
Calculate what size has the smallest internal angle of the triangle if values of angles α:β:γ = 3:4:8
- Little hand
What angle shifted little hand on the clock after one hour and 38 minutes?
In the parallelogram we know one internal angle 67°33`. Calculate the other internal angles.
Determine the size of the smallest internal angle of a right triangle which angles forming the successive members of the arithmetic sequence.
- Tree shadow
Tree perpendicular to the horizontal surface has a shadow 8.32 meters long. At the same time meter rod perpendicular to the horizontal surface has shadow 64 cm long. How tall is tree?
Mast has 9 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 9.8°. Determine the height of the mast, if the sun above the horizon is at angle 36°6'.
- Cuboid diagonal
Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 7:10:8 and if you know that the wall diagonal AC is 21 cm and angle between AC and the body diagonal AG is 40 degrees.