Planimetrics + right triangle - practice problems - page 27 of 57
Number of problems found: 1136
- Climb
For horizontal distance 4.2 km, road rise by 6.3 m. Calculate the road pitch in ‰ (permille, parts per thousand). - Determine 82470
The school building casts a shadow 16 m long on the plane of the yard, and at the same time, a vertical meter pole casts a shadow 132 cm long. Determine the height of the building. - Quadrilateral 2
Show that the quadrilateral with vertices P1(0,1), P2(4,2), P3(3,6) P4(-5,4) has two right triangles. - Consumption 80836
The right trapezoidal plot has a basic length of 102m and 86m. The vertical arm is 63 m long. Calculate the plot’s area and the mesh consumption for its fencing. - Rectangle 62854
The aspect ratio of the rectangle and its diagonal is 9:12:15. Calculate the area of the rectangle if the length of the diagonal is 105 cm. - Percentage 17613
At a horizontal distance of 800 m, the ski slope drops to 220 m above sea level. Determine the percentage decrease. - Circular segment
Calculate the area S of the circular segment and the length of the circular arc l. The height of the circular segment is 2 cm, and the angle α = 60°. Help formula: S = 1/2 r². (Β-sinβ) - Hypotenuse 80461
The ratios of the sides of a right triangle are 3: 4: 5. How long is the hypotenuse if the entire perimeter of the triangle is 48 cm? - Tree shadow 3
A 2-meter rod casts a shadow 3.2 m long. How high is a tree with a shadow of 14.4 m? - Lift
The largest angle at which the lift rises is 16°31'. Give climb angle in permille. - Uphill garden
I have a garden uphill, increasing from 0 to 4.5 m for a length of 25 m. How much is the climb in percent? - Horizontal distance
The road has a gradient of 8%. How many meters will the road rise on a horizontal distance of 400m? - The perimeter
The perimeter of equilateral △PQR is 12. The perimeter of the regular hexagon STUVWX is also 12. What is the ratio of the area of △PQR to STUVWX? - Touch circle
Point A has a distance (A, k) = 10 cm from a circle k with radius r = 4 cm and center S. Calculate: a) the distance of point A from the point of contact T if the tangent to the circle is drawn from point A b) the distance of the contact point T from the l - Three points
Three points K (-3; 2), L (-1; 4), M (3, -4) are given. Find out: (a) whether the triangle KLM is right b) calculate the length of the line to the k side c) write the coordinates of the vector LM d) write the directional form of the KM side e) write the d - The chord
A chord passing through its center is the side of the triangle inscribed in a circle. What size are the internal angles of a triangle if one of them is 40°? - The bridge
Across the circle, the lake passes through its center bridge over the lake. At three different locations on the lakeshore are three fishermen, A, B, and C. Which of the fishermen see the bridge from the largest angle? - Diagonals 81884
In an isosceles trapezoid, the basic lengths are 15 cm and 9 cm. The diagonals are 13 cm long. Calculate the perimeter and area of the trapezoid. - Parametric form
Calculate the distance of point A [2,1] from the line p: X = -1 + 3 t Y = 5-4 t Line p has a parametric form of the line equation. - Intersection 6653
Two straight paths cross, making an angle alpha = 53 degrees 30'. There are two pillars on one of them, one at the intersection, the other at a distance of 500m from it. How far does one have to go from the intersection along the other road to see both po
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