# Angle + triangle - math problems

#### Number of problems found: 388

- Inclined plane

The body stays on an inclined plane and exerts a compressive force of 70N on it. Find the angle between the inclined plane and the horizontal if a gravitational force of 100N acts on the body. - Diagonal BD

Find the length of the diagonal BD in a rectangular trapezoid ABCD with a right angle at vertex A when/AD / = 8,1 cm and the angle DBA is 42° - Telegraph poles

The bases of two adjacent telegraph poles have a height difference of 10.5 m. How long do the wires connect the two poles if the slope is 39° 30´? - Inscribed and described circle

Find the radii of a circle inscribed and circumscribed by a regular pentagon whose side measures 3 cm. - Digging a pit

The pit has the shape of a regular quadrilateral truncated pyramid. The edges of the bases are 14m and 10m long. The sidewalls form an angle of 135° with a smaller base. Determine how many m^{3}of soil were excavated when digging the pit? - The cable car

The cable car is 2610 m long and rises at an angle of 35°. Calculate the height difference between the lower and upper station of the cable car. - TV tower

Calculate the height of the television tower if an observer standing 430 m from the base of the tower sees the peak at an altitude angle of 23°? - Pentadecagon

Calculate the content of a regular 15-sides polygon inscribed in a circle with radius r = 4. Express the result to two decimal places. - Parallelogram

Find the perimeter of the parallelogram, where base a = 8 cm, height v = 3 cm, and angle alpha = 35° is the magnitude of the angle at vertex A. - Triangular prism

Calculate the surface of a regular triangular prism, the edges of the base are 6 cm long and the height of the prism is 15 cm. - 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 - Sphere in cone

A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the surface of the ball and the contents of the base is 4: 3. A plane passing through the axis of a cone cuts the cone in an isoscele - Find the

Find the content of a regular 12 sided polygon, if its side a = 12 cm. - Bisectors

As shown, in △ ABC, ∠C = 90°, AD bisects ∠BAC, DE⊥AB to E, BE = 2, BC = 6. Find the perimeter of triangle △ BDE. - Interior angles

Calculate the interior angles of a triangle that are in the ratio 2: 3: 4. - Maximum of volume

The shell of the cone is formed by winding a circular section with a radius of 1. For what central angle of a given circular section will the volume of the resulting cone be maximum? - Observation tower

From the observation tower at a height of 105 m above sea level, the ship is aimed at a depth angle of 1° 49´. How far is the ship from the base of the tower? - Sailboat

The 20 m long sailboat has an 8 m high mast in the middle of the deck. The top of the mast is fixed to the bow and stern with a steel cable. Determine how much cable is needed to secure the mast and what angle the cable will make with the ship's deck. - 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. - Powerplant chimney

From the window of the building at a height of 7.5 m, the top of the factory chimney can be seen at an altitude angle of 76° 30 ′. The base of the chimney can be seen from the same place at a depth angle of 5° 50 ′. How tall is the chimney?

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