# Triangle - examples - page 10

1. Circles 2
Calculate the area bounded by the circumscribed and inscribed circle in triangle with sides 12 cm, 14 cm, 18 cm.
2. Angles
The triangle is one outer angle 158°54' and one internal angle 148°. Calculate the other internal angles of a triangle.
3. Complete construction
Construct triangle ABC if hypotenuse c = 7 cm and angle ABC = 30 degrees. / Use Thales' theorem - circle /. Measure and write down the length of legs.
4. Angles ratio
In a triangle ABC true relationship c is less than b and b is less than a. Internal angles of the triangle are in the ratio 5:4:9. The size of the internal angle beta is:
5. Isosceles triangle
What are the angles of an isosceles triangle ABC if its base is long a=5 m and has an arm b=4 m.
6. Combi-triangle
On each side of the square is marked 10 different points outside the vertices of the square. How many triangles can be constructed from this set of points, where each vertex of the triangle lie on the other side of the square?
7. Angles in triangle
The triangle is ratio of the angles β:γ = 6:8. Angle α is 40° greater than β. What are the size of angles of the triangle?
8. Diagonals
Calculate the length of the diagonals of the rhombus if its side is long 5 and one of its internal angle is 80°.
9. Square pyramid
Calculate the volume of the pyramid with the side 5cm long and with a square base, side-base has angle of 60 degrees.
10. Euclid theorems
Calculate the sides of a right triangle if leg a = 6 cm and a section of the hypotenuse, which is located adjacent the second leg b is 5cm.
11. Trapezoid - hard example
Base of the trapezoid are: 24, 16 cm. Diagonal 22, 26 cm. Calculate its area and perimeter.
12. Moon
We see Moon in the perspective angle 28'. Moon's radius is 1740 km at the time of the full moon. Calculate the mean distance of the Moon from the Earth.
13. Mountain railway
Height difference between points A, B of railway line is 38.5 meters, their horizontal distance is 3.5 km. Determine average climb in permille up the track.
14. Height 2
Calculate the height of the equilateral triangle with side 38.
15. Internal angles
The ABCD is an isosceles trapezoid, which holds: |AB| = 2 |BC| = 2 |CD| = 2 |DA|: On its side BC is a K point such that |BK| = 2 |KC|, on its side CD is the point L such that |CL| = 2 |LD|, and on its side DA the point M is such that | DM | = 2 |MA|. Dete
16. 30-60-90
The longer leg of a 30°-60°-90° triangle measures 5. What is the length of the shorter leg?
17. Pyramid
Cuboid ABCDEFGH has dimensions AB 3 cm, BC 4 cm, CG 5 cm. Calculate the volume and surface area of a triangular pyramid ADEC.
18. Building
The building I focused at an angle 30°. When I moved 5 m building I focused at an angle 45°. What is the height of the building?
19. RT and ratio
A right triangle whose legs are in a ratio 6:12 has hypotenuse 68 m long. How long are its legs?
20. 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?

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

To this e-mail address, we will reply solution; solved examples are also published here. Please enter e-mail correctly and check whether you don't have a full mailbox.