Practice problems of the right triangle - page 49 of 81
A right triangle is a type of triangle that has one angle that measures exactly 90 degrees (a right angle). This angle is formed by the intersection of two of the triangle's sides, which are called the legs of the triangle. The other side of the triangle is called the hypotenuse, which is the side opposite the right angle, and is the longest side of the triangle. Right triangles are important in mathematics and are used in many areas of science and engineering, including trigonometry, physics, and construction. The Pythagorean theorem which states that in a right triangle, the sum of the squares of the legs (a,b) equals the square of the hypotenuse (c) is a fundamental result in geometry.Number of problems found: 1619
- Semicircle
The semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC? - Rectangle 79084
A rectangle whose one side measures 35m and the other is 7m shorter than the diagonal of the rectangle. Calculate the content in m². - Rectangular 63094
Calculate the perimeter and the area of a rectangular garden if the diagonal length is 18 m long and one of the sides of the garden is 9m long. - Metal washers
Metal washers with a diameter of 80 mm are cut from a strip of steel sheet with a width of 10 cm and a length of 2 m. When two adjacent circles meet, calculate the material waste percentage if no material is lost.
- Dimensions 39623
In the form of a pyramid with a square floor plan, the house's roof has dimensions of 12 x 12 m, at the highest point, a height of 2 m. How much roofing do we need to buy? Count on a 10% reserve. - ABCDA'B'C'D 6261
The ABCDA'B'C'D 'prism has a square base. The wall diagonal of the AC base is 9.9 cm long, and the body diagonal AC 'is 11.4 cm long. Calculate the surface area and volume of the prism. - Calculate 5499
Calculate the area of the circle, which is described by a square with a side length of 7.5 cm. - The diagonals
The diagonals in the diamond ABCD are 6 cm and 8 cm long. What is the perimeter of this diamond? - Right-angled 81359
The paths in the park form a right-angled triangle, which on the map with a scale of 1:200 has two dimensions of side lengths of 9cm and 15cm. Grandma walks this route every day for a health walk. How many meters does she walk?
- OK circle
The right triangle has hypotenuse long 33 and one cathetus long 17. Calculate the radius (circumradius) of the circle described. - Storm and roof
The roof of the building is a cone with a height of 3 meters and a radius equal to half the height of the roof. How many m² of the roof need to be repaired if 20% were damaged in a storm? - Rectangular trapezoid
How many inner right angles have a rectangular trapezoid? - Parallelogram
The sides of the parallelogram are 8 cm and 6 cm long, and the diagonals' angle is 60°. What is its area? - Perpendiculars 64574
Calculate the circle radius circumscribed by a right triangle whose perpendiculars are 10 cm and 24 cm long.
- Perpendicular 82473
In the right triangle KLM, the hypotenuse l = 9 cm and the perpendicular k = 6 cm. Calculate the size of the height vl and the line tk. - Respectively 80982
The vertices of the square ABCD are joined by the broken line DEFGHB. The smaller angles at the vertices E, F, G, and H are right angles, and the line segments DE, EF, FG, GH, and HB measure 6 cm, 4 cm, 4 cm, 1 cm, and 2 cm, respectively. Determine the ar - Surface area of the top
A cylinder is three times as high as it is wide. The length of the cylinder diagonal is 20 cm. Find the exact surface area of the top of the cylinder. - Roof 7
The roof is a regular quadrangular pyramid with a base edge of 12 m, and a height of 4 m. How many percent is folds and waste if in construction was consumed 181.4m² of the plate was? - Circumscribed circle to square
Find the length of a circle circumscribing a square side of 10 cm. Compare it to the perimeter of this square.
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