Ratio + triangle - practice problems - page 4 of 12
Number of problems found: 221
- Calculate 35223
In the ABC triangle, the angles alpha, beta, and gamma are in ratio 0.4: 0.2: 0.9. Calculate their size. - Railway embankment
The railway embankment section is an isosceles trapezoid, and the bases' sizes are in the ratio of 5:3. The arms have a length of 5 m, and the embankment height is 4.8 m. Calculates the size of the embankment section area. - 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? - Circumference 31361
The lengths of the triangle sides are in the ratio of 3:5:7. Its circumference is 45 cm. Find its lengths.
- Vertical rod
The vertical one-meter-long rod casts a shadow 150 cm long. Calculate the height of a column whose shadow is 36 m long simultaneously. - Triangle-shaped 30011
Determine the map's scale if the 1.6 km, 2.4 km, and 2.7 km triangle-shaped forests are drawn on the map as a triangle with sides of 32 mm, 48 mm, and 54 mm. - Vertical 29801
The shadow of the building is 16 m long, and the shadow of the vertical meter rod is 0.8 m long at the same time. What is the height of the building? - The straight
The straight path rises by 72 cm every 3 m of its length. How many meters will it climb to 350 m? - Sphere in cone
A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the ball's surface and the area of the base is 4:3. A plane passing through the axis of a cone cuts the cone in an isosceles triangle
- Chimney and tree
Calculate the height of the factory chimney, which casts a shadow of 6.5 m long in the afternoon. At the same time, a 6 m high tree standing near it casts a shadow 25 dm long. - Similar triangles
The triangles ABC and XYZ are similar. Find the missing lengths of the sides of the triangles. a) a = 5 cm b = 8 cm x = 7.5 cm z = 9 cm b) a = 9 cm c = 12 cm y = 10 cm z = 8 cm c) b = 4 cm c = 8 cm x = 4.5 cm z = 6 cm - Triangle 28611
The land has a triangle shape with sides of 300m, 200m, and 245m. Draw it on a scale of 1:5 000. - Equilateral cone
We pour so much water into a container with the shape of an equilateral cone, the base of which has a radius r = 6 cm, that one-third of the volume of the cone is filled. How high will the water reach if we turn the cone upside down? - Powerplant chimney
From the building window at the height of 7.5 m, we can see the top of the factory chimney at an altitude angle of 76° 30 ′. We can see the chimney base from the same place at a depth angle of 5° 50 ′. How tall is the chimney?
- Right-angled 27683
Right-angled triangle XYZ is similar to triangle ABC, which has a right angle at the vertex X. The following applies a = 9 cm, x=4 cm, x =v-4 (v = height of triangle ABC). Calculate the missing side lengths of both triangles. - Similarity coefficient
In the triangle TMA, the length of the sides is t = 5cm, m = 3.5cm, and a = 6.2cm. Another similar triangle has side lengths of 6.65 cm, 11.78 cm, and 9.5 cm. Determine the similarity coefficient of these triangles and assign similar sides to each other. - Chord of triangle
If the whole chord of the triangle is 14.4 cm long, how do you calculate the shorter and longer parts? - Meneal's 26771
Show (using Meneal's theorem) that the center of gravity divides the line in a 1:2 ratio. - Similarity 26441
How long a shadow casts a building 15 m high if the shadow of a meter rod is 90 cm? Sketch - similarity.
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