# High school + right triangle - math problems

- The tractor

The tractor sows an average of 1.5 ha per hour. In how many hours does it sows a rectangular trapezoid field with the bases of 635m and 554m and a longer arm 207m? - Depth angles

At the top of the mountain stands a castle, which has a tower 30 meters high. We see the crossroad in the valley from the top of the tower and heel at depth angles of 32° 50 'and 30° 10'. How high is the top of the mountain above the crossroad - Base of prism

The base of the perpendicular prism is a rectangular triangle whose legs length are at a 3: 4 ratio. The height of the prism is 2cm smaller than the larger base leg. Determine the volume of the prism if its surface is 468 cm^{2}. - Touch x-axis

Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis. - Trapezoid MO

The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid. - Axial section

Axial section of the cone is an equilateral triangle with area 208 dm^{2}. Calculate the volume of the cone. - Circle chord

What is the length d of the chord circle of diameter 36 m, if the distance from the center circle is 16 m? - Rectangle

The rectangle is 21 cm long and 38 cm wide. Determine the radius of the circle circumscribing rectangle. - 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: ? ? - Cuboid

Cuboid with edge a=16 cm and body diagonal u=45 cm has volume V=11840 cm^{3}. Calculate the length of the other edges. - Tetrahedral pyramid

What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=16 and height v=16? - Triangle SAS

Calculate the area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °. - Square

Points A[-5,-6] and B[7,-1] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD. - Cubes

One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm^{2}. - Cone A2V

Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm^{2}. Calculate the volume of a cone. - Gimli Glider

Aircraft Boeing 767 lose both engines at 42000 feet. The plane captain maintain optimum gliding conditions. Every minute, lose 1910 feet and maintain constant speed 211 knots. Calculate how long takes to plane from engines failure to hit ground. Calculate - River

From the observatory 11 m high and 24 m from the river bank, river width appears in the visual angle φ = 13°. Calculate width of the river. - Regular 5-gon

Calculate area of the regular pentagon with side 7 cm. - Right triangle Alef

The obvod of a right triangle is 84 cm, the hypotenuse is 37 cm long. Determine the lengths of the legs.

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