Practice problems of the right triangle - page 43 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
- Woman's day
We can easily make a heart for mothers for Woman's day by drawing two semicircles on the two upper sides of the square standing on their top. What is the radius of the circle circumscribed by this heart when the length of the side of the square is 1? - Diagonals 5113
In the diamond KLMN, the lengths of the diagonals are 10 cm and 6 cm. Determine the angle size that the longer diagonal makes with the side of the diamond. - Isosceles 7566
A right isosceles triangle is inscribed in the circle with r = 8 cm. Find triangle area S. How much percent does the triangle occupy the area of the circle? - Two heights and a side
Construct triangle ABC when the given side is c = 7 cm, height to side a va = 5 cm, and height to side b: vb = 4 cm.
- The rectangular
The rectangular trapezoid has bases 15 dm and 8 dm long, and the length of the inclined arm is 12 dm. How long is the other arm of the trapezoid? - Kites
Boys run kites on a cable of 68 meters long. What is the kite altitude if the angle from the horizontal plane is 72°? - Diamond and angles
The internal angles in the diamond are 60° and 120°. Its side is 5 cm long. Find the area of a diamond. - Rhombus
One angle of a rhombus is 136°, and the shorter diagonal is 8 cm long. Find the length of the longer diagonal and the side of the rhombus. - The rope
A 68-centimeter-long rope is used to make a rhombus on the ground. The distance between a pair of opposite side corners is 16 centimeters. What is the distance between the other two corners?
- Circle described
The circle radius described in the right triangle with a 6 cm long leg is 5 cm. Calculate the circumference of this triangle. - Raindrops
The train is moving at a speed of 60 km/h. Raindrops falling vertically in the absence of wind (with uniform movement due to the action of air resistance) leave traces on the windows of the train, deviating from the vertical direction by 30°. How fast are - Isosceles trapezium
Calculate the area of an isosceles trapezium ABCD if a = 10cm, b = 5cm, c = 4cm. - Trapezoid ABCD
Calculate the perimeter of trapezoid ABCD if we know the side c=12, b=19, which is also a height, and side d=32. - Roof cover
Above the pavilion with a square ground plan with a side length of a = 12 m is a pyramid-shaped roof with a height v = 4.5 m. Calculate how much m² of sheet metal is needed to cover this roof; if 5.5% of the sheet, we must add for joints and waste.
- Cubes
One cube is an inscribed sphere, and the other one is described. Calculate the difference of volumes of cubes if the difference of surfaces in 231 cm². - Perpendicular 32371
Calculate the area of a rectangular trapezoid whose perpendicular arm is 27 mm long and the bases are 33 mm and 19 mm long. - Calculate 16223
The following elements are known in the right triangle ABC: a = 10 cm, height to side c h = 9.23 cm. Calculate o, R (radius of the inscribed circle), r (radius of the inscribed circle). - Hypotenuse - RT
A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle? - Right-angled 64614
Arrange the given shapes according to their area content, in descending order: Square with perimeter = 16 cm A rectangle with side a = 3 cm and perimeter o = 16 cm A right-angled triangle with a hypotenuse of 4.125 cm and a hypotenuse of 8.125 cm
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