# Right triangle - high school - math problems

#### Number of problems found: 444

• Railway embankment The section of the railway embankment is an isosceles trapezoid, the sizes of the bases of which are in the ratio 5: 3. The arms have a length of 5 m and the height of the embankment is 4.8 m. Calculates the size of the embankment section area.
• Pentagonal pyramid Find the volume and surface of a regular pentagonal pyramid with a base edge a = 12.8 cm and a height v = 32.1 cm.
• Rhombus diagonals In the rhombus ABCD are given the sizes of diagonals e = 24 cm; f = 10 cm. Calculate the side length of the diamond and the size of the angles, calculate the content of the diamond
• 9-gon pyramid Calculate the volume and the surface of a nine-sided pyramid, the base of which can be inscribed with a circle with radius ρ = 7.2 cm and whose side edge s = 10.9 cm.
• Given 2 Given the following points of a triangle: P(-12,6), Q(4,0), R(-8,-6). Graph the triangle. Find triangle area.
• Bisectors As shown, in △ ABC, ∠C = 90°, AD bisects ∠BAC, DE⊥AB to E, BE = 2, BC = 6. Find the perimeter of triangle △ BDE.
• Find the 13 Find the equation of the circle inscribed in the rhombus ABCD where A[1, -2], B[8, -3] and C[9, 4].
• Embankment The railway embankment 300 m long has a cross section of an isosceles trapezoid with bases of 14 m and 8 m. The trapezoidal arms are 5 m long. Calculate how much m3 of soil is in the embankment?
• Spherical cap The spherical cap has a base radius of 8 cm and a height of 5 cm. Calculate the radius of a sphere of which this spherical cap is cut.
• Angle of cone The cone has a base diameter of 1.5 m. The angle at the main apex of the axial section is 86°. Calculate the volume of the cone.
• Hexagonal pyramid Find the volume of a regular hexagonal pyramid, the base edge of which is 12 cm long and the side edge 20 cm.
• Traffic sign There is a traffic sign for climbing on the road with an angle of 7%. Calculate at what angle the road rises (falls).
• Triangular pyramid A regular tetrahedron is a triangular pyramid whose base and walls are identical equilateral triangles. Calculate the height of this body if the edge length is a = 8 cm
• An observer An observer standing west of the tower sees its top at an altitude angle of 45 degrees. After moving 50 meters to the south, he sees its top at an altitude angle of 30 degrees. How tall is the tower?
• Cone roof How many m2 of roofing is needed to cover a cone-shaped roof with a diameter of 10 m and a height of 4 m? Add an extra 4% to the overlays.
• Distance of points A regular quadrilateral pyramid ABCDV is given, in which edge AB = a = 4 cm and height v = 8 cm. Let S be the center of the CV. Find the distance of points A and S.
• Right triangle - ratio The lengths of the legs of the right triangle ABC are in ratio b = 2: 3. The hypotenuse is 10 cm long. Calculate the lengths of the legs of that triangle.
• Perimeter and diagonal The perimeter of the rectangle is 82 m, the length of its diagonal is 29 m. Find the dimensions of the rectangle.
• 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.
• The rescue helicopter The rescue helicopter is above the landing site at a height of 180m. The site of the rescue operation can be seen from here at a depth angle of 52° 40 '. How far will the helicopter land from the rescue site?

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