Planimetrics + similarity of triangles - practice problems - page 6 of 7
Number of problems found: 129
- 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 point C, and point M lies on one-third of the side of the AC side closer to point A. Find what part of the ABC triangle contains the triangl - Identical 8831
In the triangle ABC, the point P lies closer to point A in the third of the line AB, the point R is closer to the point P in the third of the line P, and the point Q lies on the line BC so that the angles P CB and RQB are identical. Determine the ratio of - Triangle 28611
The land has a triangle shape with sides of 300m, 200m, and 245m. Draw it on a scale of 1:5 000. - Sides of the triangle
The sides of the triangle ABC have a length of 4 cm, 5 cm, and 7 cm. Construct triangle A'B'C', similar to triangle ABC, which has a circumference of 12 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: - Divide an isosceles triangle
How to divide an isosceles triangle into two parts with equal areas perpendicular to the axis of symmetry (into a trapezoid and a triangle)? - Meneal's 26771
Show (using Meneal's theorem) that the center of gravity divides the line in a 1:2 ratio. - Calculate 5148
At a distance of 10 m from the river bank, they measured the base AB = 50 m parallel to the bank. Point C on the other bank of the river is visible from point A at an angle of 32°30' and from point B at an angle of 42°15'. Calculate the width of the river - Climb
The road sign which informs the climb is 8.7%—the car drive 5 km along this road. What is the height difference that the car went?
- Mast angles and height
Calculate the height of the mast, whose foot can be seen at a depth angle of 11° and the top at a height angle of 28°. The mast is observed from a position 10 m above the level of the base of the mast. - Area and two angles
Calculate the size of all sides and internal angles of a triangle ABC if it is given by area S = 501.9; and two interior angles α = 15°28' and β = 45°. - Tower's view
From the church tower's view at the height of 65 m, the top of the house can be seen at a depth angle of alpha = 45° and its bottom at a depth angle of beta = 58°. Calculate the height of the house and its distance from the church. - Observation 82811
From the 40 m high observation deck, you can see the top of the poplar at a depth angle of 50*10' and the bottom of the poplar at a depth angle of 58*. Calculate the height of the poplar. - V-belt
Calculate the length of the V-belt when the diameter of the pulleys is: D1 = 600 mm D2 = 120 mm d = 480 mm (distance between pulley axes)
- An observer
An observer standing west of the tower sees its top at an altitude angle of 45 degrees. After moving 50 meters to the south, he sees its top at an altitude angle of 30 degrees. How tall is the tower? - Mast shadow
The mast has a 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at an angle of 15°. Determine the height of the mast if the sun above the horizon is at an angle of 33°. Use the law of sines. - A boy
A boy of height 1.7m is standing 30m away from the flagstaff on the same level ground. He observes that the angle of deviation of the top of the flagstaff is 30 degrees. Calculate the height of the flagstaff. - Boat
A force of 300 kg (3000 N) is required to pull a boat up a ramp inclined at 14° with horizontal. How much does the boat weigh? - 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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