# Examples for secondary school students - page 4

- Observer

The observer sees straight fence 100 m long in 30° view angle. From one end of the fence is 153 m. How far is it from the another end of the fence? - Proof PT

Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it. - 7 heroes

9 heroes galloping on 9 horses behind. How many ways can sort them behind? - Eiffel Tower

Eiffel Tower in Paris is 300 meters high, is made of steel. Its weight is 8000 tons. How tall is the tower model made of the same material, if it weigh is 2.4 kg? - Pipes

Water pipe has a cross-section 1405 cm^{2}. An hour has passed 756 m^{3}of water. How much water flows through the pipe with cross-section 300 cm^{2}per 15 hours if water flow same speed? - Area of RT

Calculate the area of a right triangle which hypotenuse has length 10 and one hypotenuse segment has lenght 5. - Circles

The areas of the two circles are in the ratio 2:20. The larger circle has diameter 20. Calculate the radius of the smaller circle. - Two cars

Two cars started against each other at the same time to journey long 293 km. First car went 41 km/h and second 41 km/h. What distance will be between this cars 20 minutes before meet? - Forces

In point O acts three orthogonal forces: F_{1}= 20 N, F_{2}= 7 N and F_{3}= 19 N. Determine the resultant of F and the angles between F and forces F_{1}, F_{2}and F_{3}. - Cylinders

Area of the side of two cylinders is same rectangle of 50 cm × 11 cm. Which cylinder has a larger volume and by how much? - Ace

From complete sets of playing cards (32 cards) we pulled out one card. What is the probability of pulling the ace? - Flags

How many different flags can be made from colors white, red, green, purple, orange, yellow, blue so that each flag consisted of three different colors? - Circle arc

Circle segment has a circumference of 72.95 cm and 1386.14 cm^{2}area. Calculate the radius of the circle and size of central angle. - Numbers

Determine the number of all positive integers less than 4183444 if each is divisible by 29, 7, 17. What is its sum? - Vans

In how many ways can 6 shuttle vans line up at the airport? - Right

Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ? - Triangle

Triangle KLM is given by plane coordinates of vertices: K[-12, -11] L[-15, -18] M[-13, -12]. Calculate its area and itsinterior angles. - Crystal

Crystal grows every month 1.9 promile of its mass. For how many months to grow a crystal from weight 360 g to 593 g? - Triangle ABC

Calculate the sides of triangle ABC with area 1404 cm^{2}and if a: b: c = 12:7:18 - Tractors

Fields go plow two tractors with various performance. The first tractor plow whole field in 11 hours, the second tractor plow whole field 19 hours longer. How long take plow whole field with two tractors?

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