# Right triangle - 9th grade (14y) - examples - page 7

1. Cone and the ratio Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface.
2. EQL triangle Calculate inradius and circumradius of equilateral triangle with side a=77 cm.
3. Block Calculate the volume of a cuboid ABCDEFGH if |AB| = 16 cm, |BC| = 19 cm and the angle ∠CDG = 36.9°
4. Vector Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2).
5. XY triangle Determine area of triangle given by line 7x+8y-69=0 and coordinate axes x and y.
6. Slope of the pool Calculate slope (rise:run) of the bottom of swimming pool long 10 m. Water depth at beginning of pool is 1.16 m (for children) and depth at end is 1.89 m (for swimmers). Slope express as percentage and as angle in degrees.
7. Shooter The shooter fired to a target from distance 11 m The individual concentric circle of targets have a radius increments 1 cm (25 points) by 1 point. Shot was shifted by 8'(angle degree minutes). How many points should win his shot?
8. Hexagonal prism The base of the prism is a regular hexagon consisting of six triangles with side a = 12 cm and height va = 10.4 cm. The prism height is 5 cm. Calculate the volume and surface of the prism!
9. Nine-gon Calculate the perimeter of a regular nonagon (9-gon) inscribed in a circle with a radius 13 cm. Average climb of the road is given by ratio 1:15. By what angle road average climb?
11. Height difference What height difference overcome if we pass road 1 km long with a pitch21 per mille?
12. Elevation What must be the elevation of an observer in order that he may be able to see an object on the earth 782 km away? Assume the earth to be a smooth sphere with radius 6378.1 km.
13. Triangle and its heights Calculate the length of the sides of the triangle ABC, if va=5 cm, vb=7 cm and side b is 5 cm shorter than side a.
14. Sea How far can you see from the ship's mast, whose peak is at 14 meters above sea level? (Earth's radius is 6370 km).
15. Triangular prism The base perpendicular triangular prism is a right triangle whose hypotenuse measures 5 cm and one cathetus 2 cm. Height of the prism is equal to 7/9 of the perimeter of the base. Calculate the surface area of prism.
16. Triangle KLB It is given equilateral triangle ABC. From point L which is the midpoint of the side BC of the triangle it is drwn perpendicular to the side AB. Intersection of perpendicular and the side AB is point K. How many % of the area of the triangle ABC is area o
17. Glass mosaic How many dm2 glass is nessesary to produc 39 slides of a regular 6-gon, whose side has length 23 cm? Assume that cutting glass waste is 12%.
18. Circumscribing Determine the radius of the circumscribed circle to the right triangle with legs 9 cm and 6 cm.
19. Inscribed rectangle The circle area is 216. Determine the area of inscribed rectangle with one side 5 long.
20. Distance Calculate distance between two points X[18; 19] and W[20; 3].

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