Harder math problems

River
From the observatory 18 m high and 31 m from the riverbank, river width appears in the visual angle φ = 20°. Calculate the width of the river.
Hypotenuse and height
In a right triangle is length of the hypotenuse c = 195 cm and height h_c = 70 cm. Determine the length of both triangle legs.
Sphere fall
How much percent fall volume of a sphere if the diameter decreases 3×?
Tape
Video is 199% more expensive than a tape recorder. How many percent is a tape recorder less expensive than a video?
Pizza
Pizza with a diameter of 40 cm weights 409 g. What diameter will a pizza weigh 764 g made from the same cloth (same thickness) and decorated?
Dices throws
What is the probability that the two throws of the dice: a) Six falls even once b) Six will fall at least once
Cuboid
A cuboid with edge a = 6 cm and space diagonal u = 31 cm has a volume of V = 900 cm³. Calculate the lengths of the other two edges.
Pyramid roof
3/5 of the lateral surface area of a regular quadrilateral pyramid with base edge 9 m and height 6 m has already been covered with roofing. How many square metres still need to be covered?
IS triangle
Calculate the interior angles of the isosceles triangle with base 12 cm and legs 19 cm long.
Kids
How many different ways can sit 6 boys and 3 girls in line if girls want to sit on the edge?
Area of RT
A right triangle has segments on the hypotenuse (created by the altitude) of lengths 15 cm and 9 cm. Determine the area of this triangle.
Two squares
Two squares with sides in the ratio 3:7 have a sum of their perimeters 58 cm. Calculate the sum of the area of these two squares.
Circle and angle
What is the arc length of a circle with radius r = 432 dm corresponding to a central angle of 0.53 rad?
Sphere A2V
The surface of the sphere is 241 mm². What is its volume?
Canopy
Mr Peter has a metal roof cone shape with a height of 127 cm and radius 130 cm over well. He needs to paint the roof with anticorrosion. If the manufacturer specifies the consumption of 1 kg to 3.3 m², how many kg of color must he buy?
Regular 5-gon
Calculate the area of the regular pentagon with side 16 cm.
Chess
How many ways can you select 4 fields on a classic chessboard with 64 fields so that fields don't have the same color?
School trip
The class has 19 students. How can students be accommodated in the hostel, where available 3× 2-bed, 3× 3-bed and 1× 4-bed rooms? (Each room has its unique number)
Pediatrician
Pediatrician, this month of 20 working days takes 4 days holidays. What is the probability that it will be at work on Monday?
One green
There are 45 white and 15 green balls in the container. We randomly select five balls. What is the probability that there will be one green ball maximally?

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