# Goniometry and trigonometry - math word problems - page 24 of 27

#### Number of problems found: 530

- 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]. - Base diagonal

In a regular 4-sided pyramid, the side edge forms an angle of 55° with the base's diagonal. The length of the side edge is eight meters. Calculate the surface area and volume of the pyramid. - Space diagonal angles

Calculate the angle between the body diagonal and the side edge c of the block with dimensions: a = 28cm, b = 45cm, and c = 73cm. Then, find the angle between the body diagonal and the plane of the base ABCD. - Horizontal 6161

We have a horizontal tank shaped like a rainwater cylinder, 3.45 m long and 1.7 m wide. (only up to a height of 85 cm) - Three vectors

The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point to balance. Determine the angles of each two forces. - Tower

How many m² of the copper plate should be replaced on the roof of the conical tower shape with a diameter 23 m, and the angle at the axial section's vertex is 119°? - The isosceles

The isosceles trapezoid ABCD has bases of 18 cm and 12 cm. The angle at apex A is 60°. What is the circumference and area of the trapezoid? - Angle of deviation

The surface of the rotating cone is 30 cm² (with a circle base), and its surface area is 20 cm². Calculate the deviation of this cone's side from the base's plane. - Calculate 36253

Calculate the volume of the pyramid, whose base edge a = 8 cm and the sidewall makes an angle α = 60 ° with the square base. - Block

Calculate the volume of a cuboid ABCDEFGH if |AB| = 7 cm, |BC| = 8 cm and the angle ∠CDG = 30.1° - Deviation 70434

Frustum has the base radii of the figures r1 and r2: r1> r2, r2 = s, and if the side deviation from the base plane is 60°. Express the surface and volume of the cone frustum using its side s. - Statue

On the pedestal, high 4 m is a statue 2.7 m high. At what distance from the statue must the observer stand to see it at the maximum viewing angle? Distance from the eye of the observer from the ground is 1.7 m. - Pyramid

Pyramid has a base a = 3cm and height in v = 15 cm. a) calculate the angle between plane ABV and the base plane b) calculate the angle between opposite side edges. - Spherical section cut

Find the volume of a spherical section if the radius of its base is 10 cm and the magnitude of the central angle ω = 120 degrees. - Pyramid 8

Calculate the volume and the surface area of a regular quadrangular pyramid with a base side of 9 cm and a side wall with the base has an angle of 75°. - Instantaneous 69064

Describe how the instantaneous power value in the AC circuit changes during one period. - Deviation 70744

Calculate the volume and surface of the rotating cone if its height is 10 cm and the side has a deviation of 30 ° from the base plane. - 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 - Octagonal pyramid

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

The height of a regular quadrilateral pyramid is 6.5 cm, and the angle between the base and the side wall is 42°. Calculate the surface area and volume of the body—round calculations to 1 decimal place.

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