Triangle + mean - practice problems
Number of problems found: 26
- Triangle 8320
Is there a triangle with heights of 4, 7, and 10 meters? - Angles in a triangle
The angles of the triangle ABC make an arithmetic sequence with the largest angle γ=83°. What sizes have other angles in a triangle? - Three altitudes
A triangle with altitudes 4, 5, and 6 cm is given. Calculate the lengths of all medians and all sides in a triangle. - Medians in RT
The rectangular triangle ABC has a length of 10 cm and 24 cm. Points P, Q, and R are the centers of the sides of this triangle. The perimeter of the PQR triangle is: - Coordinates 32183
The triangle ABC is given in the plane. A (-3,5), B (2,3), C (-1, -2) write the coordinates of the vectors u, v, w if u = AB, v = AC, and w = BC. Enter the coordinates of the centers of the lines SAB (..), SAC (...), SBC (. ..) - Lengths of medians from coordinates
There is a triangle ABC: A [-6.6; 1.2], B [3.4; -5.6], C [2.8; 4.2]. Calculate the lengths of its medians. - Hyperbola
Find the equation of hyperbola that passes through the point M [30; 24] and has focal points at F1 [0; 4 sqrt 6], F2 [0; -4 sqrt 6]. - Center
Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[-17,9] B[-26,-19] C[-7,7]. - Centre of mass
The vertices of triangle ABC are from the line p distances 3 cm, 4 cm, and 8 cm. Calculate the distance from the center of gravity of the triangle to line p. - Calculate 3161
In the isosceles trapezoid ABCD, the arm is 5.2 cm long, the middle bar is 7 cm long, and the height is 4.8 cm. Calculate the lengths of both bases. - Trapezoid 25
Trapezoid PART with AR||PT has (angle P=x) and (angle A=2x) . In addition, PA = AR = RT = s. Find the length of the median of Trapezoid PART in terms of s. - Right isosceles triangle
The right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into two equal segments. The length of one segment is 5 cm. What is the area of the triangle? - 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. - Two cables
On a flat plain, two columns are erected vertically upwards. One is 7 m high, and the other 4 m. Cables are stretched between the top of one column and the foot of the other column. At what height will the cables cross? Assume that the cables do not sag. - Pentagonal pyramid
Find the volume and surface of a regular pentagonal pyramid with a base edge a = 12.8 cm and a height v = 32.1 cm. - Length 26
The length of the median of the trapezoid is 10 inches. The median divides the trapezoid into two areas whose ratio is 3:5. The length of the shorter base is: - Determined 3488
Find out if there is a triangle whose two sides are 5 cm, and 8 cm long and the middle bar determined by their centers is 1.5 cm long. - Moon
We see Moon in the perspective angle 28'. Moon's radius is 1740 km at the time of the full Moon. Calculate the mean distance of the Moon from the Earth. - The triangle
Three vertices give the triangle: A [0.0] B [-4.2] C [-6.0] Calculate V (intersection of heights), T (center of gravity), O - the center of a circle circumscribed - See harmonics
Is it true that the size of the central segment of any trapezoid is the harmonic mean size of its bases? Prove it. The central segment crosses the intersection of the diagonals and is parallel to the bases.
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