# Planimetrics + reason - practice problems

#### Number of problems found: 120

- Mast

Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 13.3°. Determine the height of the mast, if the sun above the horizon is at angle 45°12'. - A drone

A flying drone aimed the area for an architect. He took off perpendicularly from point C to point D. He was at the height of 300 m above ABC's plane. The drone from point D pointed at a BDC angle of 43°. Calculate the distance between points C and B in me - Z9–I–1

In all nine fields of given shape to be filled natural numbers so that: • each of the numbers 2, 4, 6, and 8 is used at least once, • four of the inner square boxes containing the products of the numbers of adjacent cells of the outer square, • in the cir - 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. - Equilateral triangle

A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side. - Four sides of trapezoid

In the trapezoid ABCD is |AB| = 73.6 mm; |BC| = 57 mm; |CD| = 60 mm; |AD| = 58.6 mm. Calculate the size of its interior angles. - Equilateral triangle ABC

In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near the point C, and the point M lies in the one-third of the side of the AC side closer to the point A. Find what part of the ABC triangle cont - Circular railway

The railway connects in a circular arc the points A, B, and C, whose distances are | AB | = 30 km, AC = 95 km, BC | = 70 km. How long will the track from A to C? - Right triangle eq2

Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70. - River

From the observatory 11 m high and 24 m from the riverbank, river width appears in the visual angle φ = 13°. Calculate the width of the river. - Depth angles

At the top of the mountain stands a castle, which has a tower 30 meters high. We see the crossroad in the valley from the top of the tower and heel at depth angles of 32° 50 'and 30° 10'. How high is the top of the mountain above the crossroad? - Wheel gear

A drive wheel of radius 2 is connected to a drive wheel of radius 1 by a pulley of length 17. What is the distance between the wheel axles? - Poisson distribution - daisies

The meadow behind FLD was divided into 100 equally large parts. Subsequently, it was found that there were no daisies in ten of these parts. Estimate the total number of daisies in the meadow. Assume that daisies are randomly distributed in the meadow. - Clouds

Approximately at what height is the cloud we see under an angle of 26°10' and see the Sun at an angle of 29°15' and the shade of the cloud is 92 meters away from us? - Right

Determine angles of the right triangle with the hypotenuse c and legs a, b, if: 3a +4b = 4.9c - Circles

How many different circles are determined by 9 points at the plane if 6 of them lie in a straight line? - Prove

Prove that k1 and k2 are the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x^{2}+y^{2}+2x+4y+1=0 k2: x^{2}+y^{2}-8x+6y+9=0 - Divide an isosceles triangle

How to divide an isosceles triangle into two parts with equal contents perpendicular to the axis of symmetry (into a trapezoid and a triangle)? - Triangles

Ivo wants to draw all the triangles whose two sides of which have a length of 4 cm and 9 cm, and the length of the third side is expressed in whole centimeters. How many triangles does he have? - Coordinates of square vertices

I have coordinates of square vertices A / -3; 1/and B/1; 4 /. Find coordinates of vertices C and D, C and D. Thanks, Peter.

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Planimetrics - practice problems. Reason - practice problems.