Planimetrics - practice for 13 year olds - page 70 of 71
Number of problems found: 1414
- Calculate 83261
Calculate the area of the triangle ABC, in which you know the side c=5 cm, the angle at the top A= 70 degrees, and the ratio of the segments cut by the height to the side c is 1:3 - Diamond ABCD
In the diamond ABCD, the diagonal e = 24 cm, and the size of angle SAB is 28 degrees, where S is the intersection of the diagonals. Calculate the circumference of the diamond. - Ratio in trapezium
The height v and the base a, c in the trapezoid ABCD is in the ratio 1:6:3, its area S = 324 square cm. Peak angle B = 35 degrees. Determine the perimeter of the trapezoid - Cable car 2
The cable car rises at an angle of 16° and connects the upper and lower station with an altitude difference of 1082 m. How long is the track of the cable car?
- 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? - Isosceles 83247
Calculate the lengths of the sides in an isosceles triangle, given the height (to the base) Vc= 8.8cm and the angle at the base alpha= 38°40`. - 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. - Tangent of an angle
Suppose the tangent of an angle of a right-angled triangle is 0.8. Then its longest side is: - Road
Between cities A and B is a route 13 km long of average 7‰ stúpanie. Calculate the height difference between cities A and B.
- Parallelogram
We know about parallelogram ABCD: length |AB| = 76cm, |BC| = 44cm, and angle ∢BAD = 30°. Find the area of the parallelogram. - Cablecar
Funicular on Petrin (Prague) was 408 meters long and overcame the difference of 106 meters in altitude. Calculate the angle of the climb. - Tangens parallelogram
If ∠BAD between the sides AB and AD of the parallelogram is θ, what is tan θ? See diagram: A=(7,1) B=(5,-2) C=(12,1) D=(14,4) - Height difference
What height difference is overcome if we pass a road 1 km long with a pitch21 per mille? - 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.
- Inclination 43321
What percentage of the gradient should be indicated on the mark if the angle of inclination of the road is 6 ° 25'? - River
From the observatory 11 m high and 24 m from the riverbank, river width appears in the visual angle φ = 13°. Calculate the width of the river. - Wheel gear
A drive wheel of radius two is connected to a drive wheel of radius one by a pulley of length 17. What is the distance between the wheel axles? - Simple right triangle
Right triangle. Given: side c = 18.8 and angle beta = 22° 23'. Calculate sides a, b, angle alpha, and area. - Length of the chord
Calculate the length of the chord in a circle with a radius of 25 cm with a central angle of 26°.
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