Planimetrics + right triangle - practice problems - page 36 of 57
Number of problems found: 1136
- Shadow 73354
How long is the shadow of a tree 7.6 m high, and the shadow of a 190 cm high road sign is 3.3 m long? - The chimney
The chimney casts a shadow 45 meters long. The one-meter-long rod standing perpendicular to the ground has a shadow 90 cm long. Calculate the height of the chimney. - 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? - 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. - Determine 70834
At the same time, a vertical 2-meter pole casts a shadow of 0.85 meters. At the same time, a chimney of unknown height casts a 45m long shadow. Determine the height of the chimney. - Shadows
At the park, a young woman who is 1.72 meters tall casts a 3.5 meters shadow at a certain hour. What is the height of a tree in the park that, at the same time, casts a 12.3 meters shadow? - Isosceles 7566
A right isosceles triangle is inscribed in the circle with r = 8 cm. Find triangle area S. How much percent does the triangle occupy the area of the circle? - Cross road
From the junction of two streets perpendicular to each other, two cyclists (each on another street) walked out. One ran 18 km/h and the second 24 km/h. How are they away from a) 6 minutes, b) 15 minutes? - A cliff
A line from the top of a cliff to the ground passes just over the top of a pole 5 ft high. It meets the ground at a point 8 ft from the base of the pole. The point is 93 ft from the base of the cliff. How high is the cliff? - Minutes 38331
Two planes took off from Prague at one point. The first is flying north at a speed of 420 km/h, and the second is flying east at a speed of 560 km/h. How far apart will they be as the crow flies in 25 minutes of flight? - Distances 79974
The picture shows three villages, A, B, and C, and their mutual air distances. The new straight railway line is to be built so that all the villages are the same distance from the line and that this distance is the smallest possible. How far will they be - Radio radius
Two friends have shortwave radios with a range of 13 km. The first of them travels by train at a speed of 48 km per hour along a straight section of track, from which the second of the friends is 5 km away. How long will radio friends be allowed for both - Right-angled 40961
A right-angled triangle ABC has sides a = 5 cm, b = 8 cm. The similar triangle A'B'C' is 2.5 times smaller. Calculate what percentage of the area of triangle ABC is the area of triangle A'B'C'. - Calculate
Calculate the height of a tree that casts a shadow 22 m long if you know that at the same time, a pillar 2 m high casts a shadow 3 meters long. - Hexagon
There is a regular hexagon ABCDEF. If the area of the triangle ABC is 22, what is the area of the hexagon ABCDEF? I do not know how to solve it simply.... - Movement
From the crossing of two perpendicular roads started two cyclists (each on a different road). One runs at an average speed of 28 km/h, and the second 24 km/h. Determine the distance between them after 45 minutes of cycling. - Shadow 7838
A man 1.65 m tall casts a shadow of 1.25 m. How tall is the tree whose shadow is in debt 2.58 m? - Two cyclists
Two cyclists started crossing at the same time. One goes to the north speed of 20 km/h, the second eastward at a speed of 26 km/h. What will be the direct distance cycling 30 minutes from the start? - Right-angled 80745
The area of a right-angled triangle KLM with a right angle at the vertex L is 60 mm square, and its hypotenuse k is 10 mm long. Triangles KLM and RST are similar. The similarity ratio is k=2.5. Calculate the area of triangle RST. - Constructed 77874
Squares are constructed above the overhangs and the transom. Connecting the outer vertices of adjacent squares creates three triangles. Prove that their contents are the same.
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