# Right triangle - math word problems

1. Right trapezoid
The right trapezoid has bases 3.2 cm and 62 mm long. The shorter leg has a length 0.25 dm. Calculate the lengths of the diagonals and the second leg.
2. Field with vegetables
Field planted with vegetables has shape of a rectangular isosceles triangle with leg length of 24 m. At the vertices of the triangle are positioned rotating sprinklers with a range of 12 m. How much of the field sprinkler doesn't irrigated?
3. Perimeter and legs
Determine the perimeter of a right triangle if the length of one leg is 75% length of the second leg and its content area is 24 cm2.
4. High wall
I have a wall 2m high. I need a 15 degree angle (upward) to second wall 4 meters away. How high must the second wall?
5. Flowerbed
Flowerbed has the shape of a truncated pyramid, the bottom edge of the base a = 10 m, the upper base b = 9 m. Deviation angle between edge and the base is alpha = 45°. What volume is needed to make this flowerbed? How many plants can be planted if 1 m2 =.
6. Pyramid - angle
Calculate the surface of regular quadrangular pyramid whose base edge measured 6 cm and the deviation from the plane of the side wall plane of the base is 50 degrees.
7. Right triangle
Draw a right triangle ABC if |AB| = 5 cm |BC| = 3 cm, |AC| = 4 cm. Draw Thales circle above the hypotenuse of the triangle ABC.
8. Rectangular trapezoid
Calculate the content of a rectangular trapezoid with a right angle at the point A and if |AC| = 4 cm, |BC| = 3 cm and the diagonal AC is perpendicular to the side BC.
9. Tetrahedral pyramid
Calculate the volume and surface area of a regular tetrahedral pyramid, its height is \$b cm and the length of the edges of the base is 6 cm.
How many square meters is needed to cover the tower the shape of regular quadrangular pyramid base edge 10 meters, if the deviation lateral edges from the base plane is 68 °? Calculate coverage waste 10%.
11. Diamond
Side length of diamond is 35 cm and the length of the diagonal is 56 cm. Calculate the height and length of the second diagonal.
Ladder 6.4 meters long is positioned in the well such that its lower end is distanced from the wall of the well 1.2 m. The upper part of the ladder is supported on the upper edge of the well. How high is the well?
13. Rhombus 2
Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long.
14. The chord
Side of the triangle inscribed in a circle is a chord passing through circle center. What size are the internal angles of a triangle, if one of them is 40°?
15. Isosceles trapezoid
The lengths of the bases of the isosceles trapezoid are in the ratio 5:3, the arms have a length of 5 cm and height = 4.8 cm. Calculate the circumference and area of a trapezoid.
16. 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).
17. 3d vector component
The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3?
18. Concentric circles
In the circle with diameter 19 cm is constructed chord 9 cm long. Calculate the radius of a concentric circle that touches this chord.
19. Triangular pyramid
It is given perpendicular regular triangular pyramid: base side a = 5 cm, height v = 8 cm, volume V = 28.8 cm3. What is it content (surface area)?
20. Again saw
From the trunk of the tree we have to a sculpture beam with rectangular cross-section with dimensions 146 mm and 128 mm. What is the trunk smallest diameter?

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