# Right triangle - math word problems

1. SAS triangle
The triangle has two sides long 7 and 19 and included angle 36°. Calculate area of this triangle.
2. Similarity
Are two right triangles similar to each other if the first one has a acute angle 70° and second one has acute angle 20°?
3. Prism
Right angle prism, whose base is right triangle with leg a = 3 cm and hypotenuse c = 13 cm has same volume as a cube with an edge length of 3 dm. a) Determine the height of the prism b) Calculate the surface of the prism c) What percentage of the cub
4. Reverse Pythagorean theorem
Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 77 dm, 85 dm, 36 dm ? Δ DEF: 55 dm, 82 dm, 61 dm ? Δ GHI: 24 mm, 25 mm, 7 mm ? Δ JKL: 32 dm, 51 dm, 82 dm ? Δ MNO: 51 dm, 45 dm, 24 dm ?
5. Segment
Calculate the length of the segment AB, if the coordinates of the end vertices are A[10, -4] and B[5, 5].
6. Vector
Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2).
7. Height
Calculate height of the equilateral triangle if its perimeter is 8?
8. Circumscribing
Determine the radius of the circumscribed circle to the right triangle with legs 9 cm and 6 cm.
Calculate how many g's (gravity accelerations) feel glider pilot when turning the horizontal circles of radius 148 m flying at 95 km/h. Centripetal acceleration is proportional to the square of the speed and inversely proportional to the radius of rotatio
10. OK circle
Calculate the radius (circumradius) of the circle described right triangle with hypotenuse long 33 and one cathetus long 17.
11. Climb
On the road sign, which informs the climb is 8.7%. Car goes 5 km along this road. What is the height difference that car went?
12. R Trapezium
Rectangular trapezium has bases 12 and 5 and area 84 cm2. What is its perimeter?
13. Aircraft
The plane flies at altitude 6500 m. At the time of first measurement was to see the elevation angle of 21° and second measurement of the elevation angle of 46°. Calculate the distance the plane flew between the two measurements.
14. 4s pyramid
Regular tetrahedral pyramid has a base edge a=17 and collaterally edge length b=32. What is its height?
15. Reflector
Circular reflector throws light cone with a vertex angle 49° and is on 33 m height tower. The axis of the light beam has with the axis of the tower angle 30°. What is the maximum length of the illuminated horizontal plane?
16. It is rectangular?
Size of two of the angles in a triangle are: α=110°, β=40°. Is it a right triangle?
17. Tetrahedral pyramid
What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=16 and height v=16?
18. Two boats
Two boats are located from a height of 150m above the surface of the lake at depth angles of 57° and 39°. Find the distance of both boats if the sighting device and both ships are in a plane perpendicular to the surface of the lake.
19. Distance
Calculate distance between two points X[18; 19] and W[20; 3].
20. Prism
The lenght, width and height of a right prism are 17, 11 and 11 respectively. What is the lenght of the longest segment whose endpoints are vertices of the prism?

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