# Right triangle - math word problems

1. Cosine
The point (8, 6) is on the terminal side of angle θ. cos θ = ?
2. Catheti
The hypotenuse of a right triangle is 41 and the sum of legs is 49. Calculate the length of its legs.
In the square ABCD point P is in the middle of the DC side and point Q in the middle pages AD. If the area of quadrilateral BQPC is 49 cm2, what is the area of ABCD?
4. Cone and the ratio
Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface.
5. Sails
We known heights 220, 165 and 132 of sail. It has triangular shape. What is the surface of the sail?
6. RT 11
Calculate the area of right tirangle if its perimeter is p = 45 m and one cathethus is 20 m long.
8.3 meters long ladder is leaning against the wall of the well, and its lower end is 1.2 meters from this wall. How high from the bottom of a well is the top edge of the ladder?
8. Distance
Wha is the distance between the origin and the point (18; 22)?
9. Leg
Determine the area of a trapezoid with bases 71 and 42 and height is 4 shorter than the its leg.
10. Cosine
Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 3 and 8 and with the hypotenuse 8.544.
11. Inscribed rectangle
The circle area is 216. Determine the area of inscribed rectangle with one side 5 long.
12. ISO trapezium
Calculate area of isosceles trapezoid with base 95 long, leg 27 long and with the angle between the base and leg 70 degrees.
13. Chord - TS v2
The radius of circle k measures 87 cm. Chord GH = 22 cm. What is TS?
14. 30-60-90
The longer leg of a 30°-60°-90° triangle measures 5. What is the length of the shorter leg?
15. Chord - TS
The radius of circle k measures 68 cm. Arc GH = 47 cm. What is TS?
16. Isosceles IV
In an isosceles triangle ABC is |AC| = |BC| = 13 and |AB| = 10. Calculate the radius of the inscribed (r) and described (R) circle.
17. EQL triangle
Calculate inradius and circumradius of equilateral triangle with side a=77 cm.
18. Flowerbed
Flowerbed has the shape of an isosceles obtuse triangle. Arm has a size 5.5 meters and an angle opposite to the base size is 94°. What is the distance from the base to opposite vertex?
19. Semicircle
In the semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC?
20. Cable car 2
Cable car rises at an angle 41° and connects the upper and lower station with an altitude difference of 1175 m. How long is the track of cable car?

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...