Number of problems found: 526
- Central angle
What is the length of the arc of a circle with a diameter of 46 cm, which belongs to a central angle of 30°?
Approximately at what height is the cloud we see under an angle of 26°10' and see the Sun at an angle of 29°15' and the shade of the cloud is 92 meters away from us?
- Heptagonal pyramid
A hardwood for a column is in the form of a frustum of a regular heptagonal pyramid. The lower base edge is 18 cm and the upper base of 14 cm. The altitude is 30 cm. Determine the weight in kg if the density of the wood is 10 grams/cm3.
- Angles of a hexagon
Find the interior angles of a hexagon if the sizes of the angles form an arithmetic sequence and the smallest angle is 70°.
- Quadrangular pyramid
Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the side wall and the plane of the base.) S =? , V =?
Flowerbed has the shape of a truncated pyramid, the bottom edge of the base a = 10 m, the upper base b = 9 m. Deviation angle between edge and the base is alpha = 45°. What volume is needed to make this flowerbed? How many plants can be planted if 1 m2 =
- Acute triangle
In the acute triangle KLM, V is the intersection of its heights and X is the heel of height to the side KL. The axis of the angle XVL is parallel to the side LM and the angle MKL is 70°. What size are the KLM and KML angles?
- Resultant force
Calculate mathematically and graphically the resultant of a three forces with a common centre if: F1 = 50 kN α1 = 30° F2 = 40 kN α2 = 45° F3 = 40 kN α3 = 25°
A military fighter flies at an altitude of 10 km. From the ground position, it was aimed at an altitude angle of 23° and 12 seconds later at an altitude angle of 27°. Calculate the speed of the fighter in km/h.
- Black diamond run
Taleah is skiing down a black diamond run. She begins skiing at the top of a ski trail whose elevation is about 8625 feet. The ski run ends toward the base of the mountain at 3800 feet. The horizontal distance between these two points is about 4775 feet.
- Triangle from median
Calculate the perimeter, content, and magnitudes of the remaining angles of triangle ABC, given: a = 8.4; β = 105° 35 '; and median ta = 12.5.
Calculate the surface of a regular hexagonal prism whose base edge a = 12cm and side edge b = 3 dm.
- Quadrilateral pyramid
The regular quadrilateral pyramid has a base edge a = 1.56 dm and a height h = 2.05 dm. Calculate: a) the deviation angle of the sidewall plane from the base plane b) deviation angle of the side edge from the plane of the base
- Five circles
On the line segment CD = 6 there are 5 circles with radius one at regular intervals. Find the lengths of the lines AD, AF, AG, BD, and CE
Calculate the length of a semicircle with a radius of 6cm.
- Hexagonal pyramid
Please calculate the height of a regular hexagonal pyramid with a base edge of 5cm and a wall height of w = 20cm. Please sketch a picture.
- Tangents to ellipse
Find the magnitude of the angle at which the ellipse x2 + 5 y2 = 5 is visible from the point P[5, 1] .
- Three vectors
The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point so that they are in balance. Determine the angles of the each two forces.
- Inscribed and described circle
Find the radii of a circle inscribed and circumscribed by a regular pentagon whose side measures 3 cm.
- Rhombus IV
Calculate the length of the diagonals of the rhombus, whose lengths are in the ratio 1: 2 and a rhombus side is 35 cm.