# Triangle - examples - page 15

1. Perimeter of triangle
In triangle ABC angle A is 60° angle B is 90° side size c is 15 cm. Calculate the triangle circumference.
2. Right triangle trigonometrics
Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60° and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent)
3. Area of RT 2
Calculate the area of right triangle whose legs have a length 5.8 cm and 5.8 cm.
4. Equilateral triangle v2
Equilateral triangle has a perimeter 36 dm. What is its area?
5. Is right triangle
One angle of the triangle is 36° and the remaining two are in the ratio 3:5. Determine whether triangle is a rectangular triangle.
6. Angles of a triangle
In the triangle ABC, the angle beta is 15° greater than the angle alpha. The remaining angle is 30° greater than the sum of the angles alpha and beta. Calculate the angles of a triangle.
7. Smallest internal angle
Calculate what size has the smallest internal angle of the triangle if values of angles α:β:γ = 3:4:8
8. Alfa, beta, gama
In the triangle ABC is the size of the internal angle BETA 8 degrees larger than the size of the internal angle ALFA and size of the internal angle GAMA is twice the size of the angle BETA. Determine the size of the interior angles of the triangle ABC.
The size of two internal angles of a triangle ABC are α=6/18π and β=7/18π. Calculate the size of the third angle.
10. Right angled
From the right triangle with legs 12 cm and 20 cm we built a square with the same content as the triangle. How long will be side of the square?
11. Sides of the triangle
Calculate triangle sides where its area is S = 84 cm2 and a = x, b = x + 1, xc = x + 2
12. Perimeter of circle
Calculate the circumference of described circle to the triangle with sides 9,12,15 cm.
13. Three vectors
The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point so that they are in balance. Determine the angles of the each two forces.
14. QuizQ
An isosceles triangle has two sides of length 7 km and 39 km. How long is a third side?
15. Traffic laws
Under traffic regulations, car lights can illuminate the road up to a maximum of 30 m. To check the reach of the dipped-beam lights of their car, Peter stopped car at 1.5 m from the wall. The dipped-beam headlights are 60 cm high. At what height on the wa
16. Segment in a triangle
In a triangle ABC with the side/AB/ = 24 cm is constructed middle segment/DE/ = 18 cm parallel to the side AB at a distance 1 cm from AB. Calculate the height of the triangle ABC to side AB.
17. Inscribed circle
Write the equation of a incircle of the triangle KLM if K [2,1], L [6,4], M [6,1].
18. Clock face
clock face is given. Numbers 10 and 5, and 3 and 8 are connected by straight lines. Calculate the size of their angles.
19. Triangle
Determine if it is possible to construct a triangle with sides 28 31 34 by calculation.
20. Obtuse angle
The line OH is the height of the triangle DOM, line MN is the bisector of angle DMO. obtuse angle between the lines MN and OH is four times larger than the angle DMN. What size is the angle DMO? (see attached image)

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