Sine - high school - practice problems - page 3 of 10
Number of problems found: 197
- Subtracting complex in polar
Given w =√2(cosine (pi/4) + i sine (pi/4) ) and z = 2 (cosine (pi/2) + i sine (pi/2) ). What is w - z expressed in polar form? - Wheel gear
A drive wheel of radius two is connected to a drive wheel of radius one by a pulley of length 17. What is the distance between the wheel axles? - Centre of the hypotenuse
The interior angles of the triangle ABC, alpha, beta, and gamma are in a ratio of 1:2:3. The longest side of the AB triangle is 30 cm long. Calculate the perimeter of the triangle CBS if S is the center of the side AB. - Parallelogram diagonals
Find the area of a parallelogram if the diagonals u1 = 15 cm, u2 = 12 cm, and the angle formed by them is 30 degrees.
- Oscillation 48961
Write the equation of harmonic oscillation if the amplitude of the oscillation is 5 cm and its period is 0.5 s. - Square equal rhombus
Construct a square that has the same area as a rhombus ABCD if |AB| = 5cm, |AD| = 4cm and angle |DAB| = 30°. - Calculate triangle
In the triangle, ABC, calculate the sizes of all heights, angles, perimeters, and area if given a=40cm, b=57cm, and c=59cm. - Three pillars
On a straight road, three pillars are 6 m high at the same distance of 10 m. At what angle of view does Vlado see each pillar if it is 30 m from the first and his eyes are 1.8 m high? - Angle of diagonals
Calculate a rectangle's perimeter and area if its diagonal is 14 cm and the diagonals form an angle of 130°.
- Tower's view
From the church tower's view at the height of 65 m, the top of the house can be seen at a depth angle of alpha = 45° and its bottom at a depth angle of beta = 58°. Calculate the height of the house and its distance from the church. - Triangle's centroid
In the triangle ABC the given lengths of its medians tc = 9, ta = 6. Let T be the intersection of the medians (triangle's centroid), and the point S is the center of the side BC. The magnitude of the CTS angle is 60°. Calculate the length of the BC side t - Altitude angles
Cities A, B, and C lie in one elevation plane. C is 50 km east of B, and B is north of A. C is deviated by 50° from A. The plane flies around places A, B, and C at the same altitude. When the aircraft is flying around B, its altitude angle to A is 12°. Fi - 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. - The body
The body slides down an inclined plane, forming an angle α = π / 4 = 45° under the action of a horizontal plane under the effect of friction forces with acceleration a = 2.4 m/s². At what angle β must the plane be inclined so that the body slides on it af
- 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. - Isosceles 37621
In the isosceles trapezoid ABCD, its bases AB = 20cm, CD = 12cm and arms AD = BC = 8cm are given. Specify its height and alpha angle at vertex A - Oscillating 37271
Calculate the oscillation time T of the undamped harmonic oscillating motion of a particle of mass m = 10 g if the force holding the particle in this motion has a value of F = 0,05 N at a deflection of x = 3 cm. - Instantaneous 37201
The amplitude of the linear undamped harmonic oscillator is A = 12 cm, and the frequency f = 15 Hz. What is its instantaneous deflection at time a) t1 = 0.02s, b) t2 = 0.04s, when it was zero at time t = 0 s? - Inclination 34381
A skier starts down a hill of length l and an angle of inclination of 10˚. It then moves to a horizontal section of the track, which travels the same length l until it stops. Determine the coefficient of sliding friction between the skis and the snow.
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