Right triangle - 9th grade (14y) - examples - page 22

1. The mast
The top of the pole we see at an angle of 45°. If we approach the pole by 10 m, we see the top of the pole at an angle of 60°. What is the height of the pole?
The double ladder is 8.5m long. It is built so that its lower ends are 3.5 meters apart. How high does the upper end of the ladder reach?
3. Isosceles trapezium
Calculate the area of an isosceles trapezium ABCD if a = 10cm, b = 5cm, c = 4cm.
4. Cube cut
In the ABCDA'B'C'D'cube, it is guided by the edge of the CC' a plane witch dividing the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine in which ratio the edge AB is divided by this plane.
5. Tv screen
The size of a tv screen is given by the length of its diagonal. If the dimension of a tv screen is 16 inches by 14 inches, what is the size of the tv screen?
6. Rectangle diagonal
The rectangle, one side of which is 5 cm long, is divided by a 13 cm diagonal into two triangles. Calculate the area of one of these triangles in cm2.
7. RT - inscribed circle
In a rectangular triangle has sides lengths> a = 30cm, b = 12.5cm. The right angle is at the vertex C. Calculate the radius of the inscribed circle.
8. The swimmer
The swimmer swims at a constant speed of 0.85 m/s relative to water flow. The current speed in the river is 0.40 m/s, the river width is 90 m. a) What is the resulting speed of the swimmer with respect to the tree on the riverbank when the swimmer motion
9. Square
Calculate the area of the square shape of the isosceles triangle with the arms 50m and the base 60m. How many tiles are used to pave the square if the area of one tile is 25 dm2?
10. Axial cut of a rectangle
Calculate the volume and surface of the cylinder whose axial cut is a rectangle 15 cm wide with a diagonal of 25 cm long.
11. Waste
How many percents are waste from a circular plate with a radius of 1 m from which we cut a square with the highest area?
12. Right triangle
Ladder 16 feet reaches up 14 feet on a house wall. The 90-degree angle at the base of the house and wall. What are the other two angles or the length of the leg of the yard?
13. Depth angle
From a cliff of 150 meters high, we can see the ship at a depth angle of 9° at sea. How far is the ship from the cliff?
14. A truck
A truck departs from a distribution center. From there, it goes 20km west, 30km north and 10km west and reaches a shop. How can the truck reach back to the distribution center from the shop (what is the shortest path)?
Adam placed the ladder of the house, the upper end reaching to the window at the height of 3.6m, and the lower end standing on level ground and was distant from a wall of 1.5m. What is the length of the ladder?
16. Pavement
Calculate the length of the pavement that runs through a circular square with a diameter of 40 m if distance the pavement from the center is 15 m.
17. Cube cut
The cube ABCDA'B'C'D ' has an edge of 12cm. Calculate the area of diagonal cut B DD'B '.
18. Spherical cap
Place a part of the sphere on a 4.6 cm cylinder so that the surface of this section is 20 cm2. Determine the radius r of the sphere from which the spherical cap was cut.
19. An angle
An angle x is opposite side AB which is 10, and side AC is 15 which is hypotenuse side in triangle ABC. Calculate angle x.
20. Pyramid height
Find the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height h = 20cm.

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