# Right triangle - math word problems

- SAS triangle

The triangle has two sides long 7 and 19 and included angle 36°. Calculate area of this triangle. - 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°? - 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 - 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 ? - Segment

Calculate the length of the segment AB, if the coordinates of the end vertices are A[10, -4] and B[5, 5]. - Vector

Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2). - Height

Calculate height of the equilateral triangle if its perimeter is 8? - Circumscribing

Determine the radius of the circumscribed circle to the right triangle with legs 9 cm and 6 cm. - Overload

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 - OK circle

Calculate the radius (circumradius) of the circle described right triangle with hypotenuse long 33 and one cathetus long 17. - 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? - R Trapezium

Rectangular trapezium has bases 12 and 5 and area 84 cm^{2}. What is its perimeter? - 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. - 4s pyramid

Regular tetrahedral pyramid has a base edge a=17 and collaterally edge length b=32. What is its height? - 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? - It is rectangular?

Size of two of the angles in a triangle are: α=110°, β=40°. Is it a right triangle? - Tetrahedral pyramid

What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=16 and height v=16? - 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. - Distance

Calculate distance between two points X[18; 19] and W[20; 3]. - 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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