# Right triangle - math word problems

1. Diagonals of diamond Find the area and circumference of the diamond ABCD with 15m and 11m diagonals.
2. Two aircraft From the airport will start simultaneously two planes, which fly tracks are perpendicular to each other. The first flying speed of 680 km/h and the second 840 km/h. Calculate how far the aircraft will fly for half an hour. 4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall?
4. How far From the top of a lighthouse 145 ft above sea level, the angle of depression of a boat 29°. How far is the boat from the lighthouse?
5. Rhombus One angle of a rhombus is 136° and the shorter diagonal is 8 cm long. Find the length of the longer diagonal and the side of the rhombus.
6. Rectangular trapezoid The rectangular trapezoid ABCD is: /AB/ = /BC/ = /AC/. The length of the median is 6 cm. Calculate the circumference and area of a trapezoid.
7. The rope A 68 centimetre long rope is used to make a rhombus on the ground. The distance between a pair of opposite side corners is 16 centimetres what is the distance between the other two corners?
8. Ratio iso triangle The ratio of the sides of an isosceles triangle is 7:6:7 Find the base angle to the nearest answer correct to 3 significant figure.
9. Midpoints Triangle ABC with sides a = 5 cm, b = 3 cm, c = 40mm has a midpoint of K, L, M. How many centimeters is long perimeter of parallelogram KBLM?
10. Ruler How far from Peter stands 2m hight John? Petr is looking to John over ruler that keeps at arm's distant 60 cm from the eye and on the ruler John measured the height of 15 mm.
11. Triangle ABC v2 Area of the triangle is 12 cm square. Angle ACB = 30º , AC = (x + 2) cm, BC = x cm. Calculate the value of x. Tree perpendicular to the horizontal surface has a shadow 8.32 meters long. At the same time meter rod perpendicular to the horizontal surface has shadow 64 cm long. How tall is tree?
13. Four sided prism Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50 degree angle with the base plane.
14. Pentagon Calculate the length of side, circumference and area of a regular pentagon, which is inscribed in a circle with radius r = 6 cm.
15. Rectangle 3-4-5 The sides of the rectangle are in a ratio of 3:4. The length of the rectangle diagonal is 20 cm. Calculate the content of the rectangle.
16. Regular n-gon Which regular polygon have a radius of circumscribed circle r = 10 cm and the radius of inscribed circle p = 9.962 cm?
17. Cube and sphere Cube with the surface area 150 cm2 is described sphere. What is sphere surface?
18. Rhombus and diagonals The a rhombus area is 150 cm2 and the ratio of the diagonals is 3:4. Calculate the length of its height.
19. Medians and sides Triangle ABC in the plane Oxy; are the coordinates of the points: A = 2.7 B = -4.3 C-6-1 Try calculate lengths of all medians and all sides.
20. Two cyclists Two cyclists started from crossing in the same time. One goes to the north speed 20 km/h, the second eastward at speed 26 km/h. What will be the direct distance cycling 30 minutes from the start?

Do you have an interesting mathematical word problem that you can't solve it? Enter it, and we can try to solve it.

We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...