# Triangle - examples - page 18

1. Acceleration 2 if a car traveling at a velocity of 80 m/s/south accelerated to a velocity of 100 m/s east in 5 seconds, what is the cars acceleration? using Pythagorean theorem
2. Pyramid 4sides Calculate the volume and the surface of a regular quadrangular pyramid when the edge of the base is 4 cm long and the height of the pyramid is 7 cm.
3. Prism Find the volume and surface area of prism with base of an equilateral triangle with side 7 dm long and the body height of 1.5 m.
4. Diagonal - simple Calculate the length of the diagonal of a rectangle with dimensions 5 cm and 12 cm.
5. Sides od triangle Sides of the triangle ABC has length 4 cm, 5 cm and 7 cm. Construct triangle A'B'C' that are similar to triangle ABC which has a circumference of 12 cm.
6. Triangles Find out whether given sizes of the angles can be interior angles of a triangle: a) 23°10',84°30',72°20' b) 90°,41°33',48°37' c) 14°51',90°,75°49' d) 58°58',59°59',60°3'
7. Sines In ▵ ABC, if sin(α)=0.5 and sin(β)=0.6 calculate sin(γ)
8. Isosceles - isosceles It is given a triangle ABC with sides /AB/ = 3 cm /BC/ = 10 cm, and the angle ABC = 120°. Draw all points X such that true that BCX triangle is an isosceles and triangle ABX is isosceles with the base AB.
9. Drainage channel The cross section of the drainage channel is an isosceles trapezoid whose bases have a length of 1.80 m, 0.90 m and arm has length 0.60 meters. Calculate the depth of the channel.
10. Bearing A plane flew 50 km on a bearing 63°20' and the flew on a bearing 153°20' for 140km. Find the distance between the starting point and the ending point.
11. Parcel parcel has a rectangular shape of a trapezoid with bases 12 m and 10 m and a height 8 m. On parcel was built object with a footprint an isosceles triangle shape with side 4 m and height three-quarters of a meter. What is the area of unbuild parcel?
12. Equilateral triangle v3 Calculate the content of the colored gray part. Equilateral triangle has side length 8 cm. Arc centers are the vertices of a triangle.
13. Ethernet cez ulicu Karol a Jozef sú vášniví hráči počítačových hier a býva v domoch, ktoré sú presne naproti sebe cez ulicu, takže si vidia navzájom do okien. Rozhodli sa, že si svoje počítače prepoja telefónnym káblom aby mohli hrať spoločne hry. Karol býva v prvom poschodí
14. Medians and sides Determine the size of a triangle KLM and the size of the medians in the triangle. K=(-5; -6), L=(7; -2), M=(5; 6).
15. Angles in triangle Calculate the alpha angle in the triangle if beta is 61 degrees and 98 gamma degrees.
16. Triangle KLM In the rectangular triangle KLM, where is hypotenuse m (sketch it!) find the length of the leg k and the height of triangle h if hypotenuse's segments are known mk = 5cm and ml = 15cm
17. Triangle Determine whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the triangle. a = 158 b = 185 c = 201
18. The mast A 40 m high mast is secured in half by eight ropes of 25 m long. The ends of the ropes are equidistant from each other. Calculate this distance.
19. Triangle ABC v2 Area of the triangle is 12 cm square. Angle ACB = 30º , AC = (x + 2) cm, BC = x cm. Calculate the value of x.
20. Medians and sides Triangle ABC in the plane Oxy; are the coordinates of the points: A = 2.7 B = -4.3 C-6-1 Try calculate lengths of all medians and all sides.

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