Basic operations and concepts - math word problems - page 328 of 331

Number of problems found: 6620

Cablecar
Funicular on Petrin (Prague) was 408 meters long and overcame the difference of 106 meters in altitude. Calculate the angle of the climb.
Railway
The railway line had a 5.8 km segment climb nine per mille. How many meters does the track ascent?
Intersect of 10 lines
At how many points do ten lines intersect if no two are parallel?
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?
Chord 24
A chord of length t = r√2 divides a circle with radius r into two circular segments. What is the ratio of the areas of these two segments?
Calculate
Calculate the area of triangle ABC if given by alpha = 49°, beta = 31°, and the height on the c side is 9 cm.
Lift
The largest angle at which the lift rises is 16°31'. Give climb angle in per mille.
Clouds
We see the cloud under an angle of 26°10' and the Sun at an angle of 29°15'. The shade of the cloud is 92 meters away from us. Approximately at what height is the cloud?
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?
Altitude difference
Between the resorts is 15 km, and the climb is 13 per mille. What is the height difference?
Four sides of trapezoid
In the trapezoid ABCD is |AB| = 73.6 mm; |BC| = 57 mm; |CD| = 60 mm; |AD| = 58.6 mm. Calculate the size of its interior angles.
Depth angles
At the top of the mountain stands a castle with a tower 30 meters high. We see the crossroad at a depth angle of 32°50' and the heel at 30°10' from the top of the tower. How high is the top of the mountain above the crossroad?
Right triangle eq2
Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
Perimeter - ASA theorem
Calculate the perimeter of the triangle ABC if a = 12 cm, the angle beta is 38 degrees, and the gamma is 92 degrees.
Right
Determine the angles of a right triangle with hypotenuse c and legs a and b, if: 2a +5b = 5.283c
Rhombus 48
A large rhombus is composed of four identical smaller rhombuses, each with an area of 42 m² and an angle alpha of 60°. What is the perimeter of the large rhombus?
Traffic sign
There is a traffic sign for climbing on the road with an angle of 7%. Calculate at what angle the road rises (falls).
Stairway
What angle rising stairway if the step height is 20 cm and the width 26 cm?
Triangle area and angle
Calculate the area of the triangle ABC, in which you know the side c=5 cm, the angle at the vertex A= 70 degrees, and the ratio of the segments cut by the height to the side c is 1:3 .
Angle of inclination
What percentage of the gradient should be indicated on the mark if the angle of inclination of the road is 6°25'?

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