# Right triangle - high school - math problems

#### Number of problems found: 427

- 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 m^{3}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. - 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 m^{2}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. - 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? - Tetrahedral pyramid 8

Let’s all side edges of the tetrahedral pyramid ABCDV be equally long and its base let’s be a rectangle. Determine its volume if you know the deviations A=40° B=70° of the planes of adjacent sidewalls and the plane of the base and the height h=16 of the p - Octagonal pyramid

Find the volume of a regular octagonal pyramid with height v = 100 and the angle of the side edge with the plane of the base is α = 60°. - Tropics and polar zones

What percentage of the Earth’s surface lies in the tropical, temperate and polar zone? Individual zones are bordered by tropics 23°27' and polar circles 66°33' - An equilateral

An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle? - Inclined plane

1. How much work W we have to do to pull a body weighing 200 kg along an inclined plane with a length of 4 m to a total height of 1.5 m. 2. Find the force we need to exert to do this if we neglect frictional resistance. 3. Find the force we would need i - Which

Which of the following numbers most accurately area of a regular decagon with side s = 2 cm? (A) 9.51 cm^{2}(B) 20 cm^{2}(C) 30.78 cm^{2}(D) 31.84 cm^{2}(E) 32.90 cm^{2} - Regular hexagonal prism

Calculate the volume of a regular hexagonal prism whose body diagonals are 24cm and 25cm long.

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