# Cosine + Pythagorean theorem - math problems

#### Number of problems found: 58

- Centre of the hypotenuse

For 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. - 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°. - Angle of diagonals

Calculate the perimeter and the area of a rectangle if its diagonal is 14 cm and the diagonals form an angle of 130°. - Altitude angles

Cities A, B, C lie in one elevation plane. C is 50 km east of B, B is north of A. C is deviated by 50° from A. The plane flies around places A, B, C at the same altitude. When the aircraft is flying around B, its altitude angle to A is 12°. Find the altit - 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 vectors 3D

The vectors u = (1; 3; -4), v = (0; 1; 1) are given. Find the size of these vectors, calculate the angle of the vectors, the distance between the vectors. - Ratio in trapezium

The height v and the base a, c in the trapezoid ABCD are in the ratio 1: 6: 3, its content S = 324 square cm. Peak angle B = 35 degrees. Determine the perimeter of the trapezoid - 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, calculate the content of the diamond - Right triangle

A right triangle ABC is given, c is a hypotenuse. Find the length of the sides a, b, the angle beta if c = 5 and angle alfa = A = 35 degrees. - 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. - 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 length of the arm is 17 cm and the height to the base is 12 cm. - Angle of the body diagonals

Using vector dot product calculate the angle of the body diagonals of the cube. - 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 the radius R = 6370 km - Tetrahedral pyramid

Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30'. - The aspect ratio

The aspect ratio of the rectangular triangle is 13: 12: 5. Calculate the internal angles of the triangle.

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Pythagorean theorem is the base for the right triangle calculator. Cosine - math problems. Pythagorean theorem - math problems.