# Triangle - examples - page 27

1. 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
2. SSA and geometry
The distance between the points P and Q was 356 m measured in the terrain. The PQ line can be seen from the viewer at a viewing angle of 107° 22 '. The observer's distance from P is 271 m. Determine the viewing angle of P and observer.
3. 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.
4. 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?
5. 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?
6. 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)?
7. 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?
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?
9. 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.
10. 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.
11. 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.
12. Surface area 6
Find the surface area of a prism whose bases are right triangles with sides of length 3, 4, and 5 inches and a height of 8 inches. Include a sketch
13. Cube cut
The cube ABCDA'B'C'D ' has an edge of 12cm. Calculate the area of diagonal cut B DD'B '.
14. Three sides
Side b is 2 cm longer than side c, side a is 9 cm shorter than side b. The triangle circumference is 40 cm. Find the length of sides a, b, c . .. .
15. Spruce height
How tall was spruce that was cut at an altitude of 8m above the ground and the top landed at a distance of 15m from the heel of the tree?
16. Hexagon ABCDEF
In the regular hexagon ABCDEF, the diagonal AE has a length 8cm. Calculate the circumference and the hexagon area.
17. Tetrahedral pyramid
Calculate the surface S and the volume V of a regular tetrahedral pyramid with the base side a = 5 m and a body height of 14 m.
18. Complementary angles 2
Two complementary angles are (x+4) and (2x - 7) find the value of x
19. Sss triangle
Calculate the area and heights in the triangle ABC by sides a = 8cm, b = 11cm, c = 12cm
20. Isosceles trapezoid
The old father decided to change the top plate of an isosceles-like trapezoid with the basic dimensions of 120 cm and 60 cm, and the shoulder is 50 centimeters long. How much does it pay for a new plate and a square meter worth 17 euros?

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