# Right triangle - 8th grade (13y) - examples - page 6

1. XY triangle
Determine area of triangle given by line 7x+8y-69=0 and coordinate axes x and y.
2. 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.
3. 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!
4. 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?
5. Nine-gon
Calculate the perimeter of a regular nonagon (9-gon) inscribed in a circle with a radius 13 cm.
6. Height difference
What height difference overcome if we pass road 1 km long with a pitch21 per mille?
Average climb of the road is given by ratio 1:15. By what angle road average climb?
8. Elevation
What must be the elevation of an observer in order that he may be able to see an object on the earth 536 km away? Assume the earth to be a smooth sphere with radius 6378.1 km.
9. 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).
10. Triangular prism
Calculate the surface area and volume of a triangular prism, base right triangle if a = 3 cm, b = 4 cm, c = 5 cm and height of prism h=12 cm.
11. The bridge
Across the circle lakepasses through its center bridge over the lake. At three different locations on the lake shore are three fishermen A, B, C. Which of fishermen see the bridge under the largest angle?
12. 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
13. Cathethus and the inscribed circle
In a right triangle is given one cathethus long 14 cm and the radius of the inscribed circle of 5 cm. Calculate the area of this right triangle.
14. Box
Calculate the angle between box base 9 x 14 and body diagonal length 18.
15. Circumscribing
Determine the radius of the circumscribed circle to the right triangle with legs 9 cm and 6 cm.
16. Distance
Calculate distance between two points X[18; 19] and W[20; 3].
17. Glass mosaic
How many dm2 glass is nessesary to produc 97 slides of a regular 6-gon, whose side has length 21 cm? Assume that cutting glass waste is 10%.
18. Inscribed rectangle
The circle area is 216. Determine the area of inscribed rectangle with one side 5 long.
19. Triangular prism
Base of perpendicular triangular prism is a right triangle with leg length 5 cm. Content area of the largest side wall of its surface is 130 cm² and the height of the body is 10 cm. Calculate its volume.
20. Felix
Calculate how much land saw Felix Baumgartner after jump from 32 km above ground. The radius of the Earth is R = 6378 km.

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