Practice problems of the right triangle - page 42 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
- Perpendicular 70824
One perpendicular to the ABC right triangle has a length a = 14 cm, and a radius of the circle inscribed in this triangle r = 5 cm. Find the size of the diaphragm and its second perpendicular. - Reflector
The circular reflector throws a light cone with a vertex angle 49° and is on 33 m height tower. The axis of the light beam has the axis of the tower angle 30°. What is the maximum length of the illuminated horizontal plane? - Trapezoid
The rectangular trapezoid ABCD with a right angle at the vertex A has sides a, b, c, and d. Calculate the circumference and the area of the trapezoid if given: a = 25cm, c = 10cm, d = 8cm - Isosceles trapezoid
What is the height of an isosceles trapezoid, the base of which has a length of 11 cm and 8 cm and whose legs measure 2.5 cm?
- Hypotenuses 83154
In a right-angled triangle ABC with a right angle at the vertex C, the magnitudes of the hypotenuses are given ta=5, tb=2√10. Calculate the side sizes of triangle ABC and the circle's radius described by this triangle. - Calculate 48073
Calculate the area of the isosceles trapezoid ABCD if a = 14 cm, c = 8 cm, and the size of the angle DAB is 52 °. - Right 24
The right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into two unequal segments. The length of one segment is 5 cm. What is the area of the triangle? Thank you. - Isosceles trapezoid
Find the area of an isosceles trapezoid; if the bases are 12 cm and 20 cm, the arm's length is 16 cm. - Infinity
A square with a side 19 long is an inscribed circle, and the circle is inscribed next square, circle, and so on to infinity. Calculate the sum of the area of all these squares.
- A kite
ABCD is a kite. Angle OBC = 20° and angle OCD = 35°. O is the intersection of diagonals. Find angle ABC, angle ADC and angle BAD. - Drainage channel
The cross-section of the drainage channel is an isosceles trapezoid whose bases have a length of 1.80 m and 0.90 m, and the arm has a length of 0.60 meters. Calculate the depth of the channel. - ISO trapezium
Calculate the area of an isosceles trapezoid with base 95 long, leg 27 long, and with the angle between the base and leg 70 degrees. - Iglu - cone tent
The cone-shaped tent is 3 m high, and the diameter of its base is 3.2 m. a) The tent is made of two layers of material. How many m² of fabric is needed for production (including flooring) if 20% needs to be added to the minimum amount due to cutting waste - Circumference 1608
The bases of the isosceles trapezoid measure 110m and 50m. The distance between the bases is 40m. Calculate its circumference.
- Isosceles trapezoid
Calculate the circumference and the area of the isosceles trapezoid if you know the size of the bases is 8 and 12 cm, and the size of the arms is 5 cm. - Hexagon ABCDEF
In the regular hexagon ABCDEF, the diagonal AE has a length of 8cm. Calculate the circumference and the hexagon area. - Diagonals 3580
Cube edge length 5cm. Draw different diagonals. - Rhombus and diagonals
The rhombus area is 150 cm2, and the ratio of the diagonals is 3:4. Calculate the length of its height. - Right-angled 78394
A right-angled triangle was inscribed in a circle with a diameter of 20 cm, whose hypotenuse is the circle's diameter and has the largest possible area. Calculate the area of this triangle.
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