Planimetrics + system of equations - practice problems - page 13 of 14
Number of problems found: 263
- Bases
The length of the bases trapezium is in ratio 4:5. The length of the midline is 15. How long are the bases of a trapezoid? - Circle - analytics geometry
Write the equation of the circle that passes through the points Q[3.5] R[2.6] and has its center on the line 2x+3y-4=0. - Coordinate 82580
Write the equation of the ellipse that passes through the points, and its axes are identical to the coordinate axes when A = [2, 3] and B = [−1, −4]. - Angles in a triangle
The angles of the triangle ABC make an arithmetic sequence with the largest angle γ=83°. What sizes have other angles in a triangle?
- Circumference 9811
Kristýna chose a certain odd natural number divisible by three. Jakub and David then examined triangles with a circumference in millimeters equal to the number selected by Kristýna and whose sides have lengths in millimeters expressed by different integer - Pasture 79214
I need to find out the number of bulls in the third period. In the first period, 12 bulls grazed on 3 and 1/3 ha for 4 weeks. In the second period, 21 bulls graze on 10 ha for 9 weeks. How many bulls in the third period graze for 24ha and 18 weeks? The pa - An archer
An archer stands 60 meters (m) from a target. She launches an arrow that lands 3 centimeters (cm) from the bull's eye. The archer changes her position to 40 m from the target, and her next arrow lands 2 cm from the bull's eye. She changes her position to - Triangle midpoints
Determine coordinates of triangle ABC vertices if we know triangle sides midpoints SAB [0;3] SBC [1;6] SAC [4;5], its sides AB, BC, AC. - Side lengths
In the triangle ABC, the height to side a is 6cm. The height to side b is equal to 9 cm. Side "a" is 4 cm longer than side "b". Calculate the side lengths a, b.
- 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: - Intersection 5413
In the acute triangle KLM, the angle KLM is 68°. Point V is the intersection of the altitudes, and P is the foot of the altitude on the side LM. The angle P V M axis is parallel to the side KM. Compare the sizes of angles MKL and LMK. - Parallelogram
The sides of the parallelogram are 8 cm and 6 cm long, and the diagonals' angle is 60°. What is its area? - Clouds
From two points, A and B, on the horizontal plane, a forehead cloud was observed above the two points under elevation angles 73°20' and 64°40'. Points A and B are separated by 2830 m. How high is the cloud? - Circular sector
I have a circular sector with a length of 15 cm with an unknown central angle. It is created from a circle with a radius of 5 cm. What is the central angle alpha in the circular sector?
- Trapezoid: 18703
In the ABCD trapezoid: | AD | = | CD | = | BC | a | AB | = | AC |. Determine the size of the delta angle. - Height of the arc - formula
Calculate the arc's height if the arc's length is 77 and chord length 40. Does exist a formula to solve this? - Largest angle of the triangle
Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a - 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 - The tower
The observer sees the tower's base 96 meters high at a depth of 30 degrees and 10 minutes and the top of the tower at a depth of 20 degrees and 50 minutes. How high is the observer above the horizontal plane on which the tower stands?
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