Sine + Pythagorean theorem - practice problems - page 2 of 5
Number of problems found: 87
- 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. - Rectangle 49153
Rectangle ABCD, whose | AB | = 5cm, | AC | = 8 cm, ∢ | CAB | = 30 °. How long is the other party, and what is its area? - Length of the chord
Calculate the length of the chord in a circle with a radius of 25 cm with a central angle of 26°. - Rectangular
Rectangular triangle KLM with right angle at vertex L, angle beta at vertex K, and angle alpha at vertex M. Angle at vertex M = 65°, side l = 17.5 cm. Use Pythagorean theorems and trigonometric functions to calculate the lengths of all sides and the angle - Angle of diagonals
Calculate a rectangle's perimeter and area if its diagonal is 14 cm and the diagonals form an angle of 130°. - 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. - Ratio in trapezium
The height v and the base a, c in the trapezoid ABCD is in the ratio 1:6:3, its area S = 324 square cm. Peak angle B = 35 degrees. Determine the perimeter of the trapezoid - 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 - 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. - 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, and calculate the area of the diamond. - Right triangle
A right triangle ABC is given, and c is a hypotenuse. Find the length of the sides a, b, the angle beta if c = 5 and angle alfa = A = 35 degrees. - 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. - Right angle
In a right triangle ABC with a right angle at the apex C, we know the side length AB = 24 cm and the angle at the vertex B = 71°. Calculate the length of the legs of the triangle. - Triangle in a square
In a square ABCD with side a = 6 cm, point E is the center of side AB, and point F is the center of side BC. Calculate the size of all angles of the triangle DEF and the lengths of its sides. - The right triangle
In the right triangle ABC with a right angle at C, we know the side lengths AC = 9 cm and BC = 7 cm. Calculate the length of the remaining side of the triangle and the size of all angles. - Isosceles triangle
Calculate the size of the interior angles and the length of the base of the isosceles triangle if the arm's length is 17 cm and the height of the base is 12 cm. - Circumscribed 22713
Calculate the circumference and the area of a regular ten-angle polygon if the radius of the circumscribed circle r = 20 cm. - What percentage
What percentage of the Earth's surface is seen by an astronaut from a height of h = 350 km? Take the Earth as a sphere with a radius R = 6370 km.
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