Practice problems of the right triangle - page 61 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
- The cone
The cone has a base radius of 12 cm and a height of 20 cm. It was truncated at 6 cm from the base. We created a truncated cone - frustum. Find the radius of the base of the truncated cone. - Slant height
The cone's slant height is 5cm, and the radius of its base is 3cm, so find the cone's volume. - A circle 2
A circle is centered at the point (-7, -1) and passes through the point (8, 7). The radius of the circle is r units. The point (-15, y) lies in this circle. What are r and y (or y1, y2)? - Find parameters
Find parameters of the circle in the plane - coordinates of center and radius: x²+(y-3)²=14 - Cuboid diagonal
Calculate the volume and surface area of the cuboid ABCDEFGH, which sides a, b, and c has dimensions in the ratio of 7:8:10. If you know that the diagonal wall AC is 56 cm, and the angle between AC and space diagonal AG is 25 degrees. - Rhombus and diagonals
The lengths of the diamond diagonals are e = 48cm f = 20cm. Calculate the length of its sides. - Rhombus IV
Calculate the length of the diagonals of the rhombus, whose sizes are in the ratio of 1:2 and a rhombus side is 35 cm. - Rectangular base pyramid
The pyramid has a rectangular base of 2.8 m and 1.4 m and a height of 2.5 meters. Calculate an area of the shell of the pyramid. - Calculate 8326
Calculate the cone shell with a base diameter of 40 cm and a cone height of 50 cm. - Spherical cap 4
What is the surface area of a spherical cap, the base diameter of 20 m, and the height of 2.5 m? Calculate using the formula. - Top of the tower
The top of the tower has the shape of a regular hexagonal pyramid. The base edge has a length of 1.2 m. The pyramid height is 1.6 m. How many square meters of sheet metal are needed to cover the top of the tower if 15% extra sheet metal is needed for join - Hypotenuse 64694
Point S is the center of the hypotenuse AB of the right triangle ABC. Calculate the content of triangle ABC if the line on the hypotenuse is 0.2 dm long and if | ∢ACS | = 30 °. - Embankment 2539
The profile of the railway embankment has the shape of an isosceles trapezoid, where a = 16.4 m, c = 10.6 m, and b = d = 5.2 m. Calculate the embankment height. - Construct
Construct a rhombus ABCD if the size of the diagonal AC is 6 cm and the diagonal BD is 8 cm long. - Sphere cuts
At what distance from the center intersects the sphere with radius R = 91 plane if the cut area and area of the main sphere circle are in ratio 3/6? - Rectangular trapezoid
The ABCD rectangular trapezoid with the AB and CD bases is divided by the diagonal AC into two equilateral rectangular triangles. The length of the diagonal AC is 62cm. Calculate the trapezium area in cm square and calculate how many different perimeters - Quadrilateral
In the square ABCD point, P is in the middle of the DC side, and point Q is in the middle of side AD. If the area of quadrilateral BQPC is 76 cm², what is the area of ABCD? - Cuboidal room
The length of the cuboidal room is 2m the breadth of the cuboidal room is 3m and height is 6m find the length of the longest rod that can be fitted in the room - The spacecraft
The spacecraft spotted a radar device at an altitude angle alpha = 34 degrees 37 minutes and had a distance of u = 615km from Earth's observation point. Calculate the distance d of the spacecraft from Earth at the moment of observation. Earth is considere - Diagonals
A diagonal of a rhombus is 20 cm long. If its side is 26 cm, find the length of the other diagonal.
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