# Triangle - examples - page 12

1. Diagonal
Can be a diagonal of diamond twice longer than it side?
2. Angle
Draw angle |∠ ABC| = 130° and built its axis. What angle is between axis angle and arm of angle?
3. Triangle P2
Can triangle have two right angles?
4. Angles of the triangle
ABC is a triangle. The size of the angles alpha, beta are in a ratio 4: 7. The angle gamma is greater than the angle alpha by a quarter of a straight angle. Determine angles of the triangle ABC.
5. Maple
Maple peak is visible from a distance 3 m from the trunk from a height of 1.8 m at angle 62°. Determine the height of the maple.
6. Angles ratio
The internal angles of a triangle are in ratio 1:4:5 What kind of triangle is it? (solve internal angles and write down and discuss)
7. Reflector
Circular reflector throws light cone with a vertex angle 49° and is on 33 m height tower. The axis of the light beam has with the axis of the tower angle 30°. What is the maximum length of the illuminated horizontal plane?
8. Triangular pyramid
Determine the volume and surface area of a regular triangular pyramid having a base edge a=20 cm and a lateral edge b = 35 cm
9. Inclined plane
On the inclined plane with an angle of inclination of 30 ° we will put body (fixed point) with mass 2 kg. Determine the acceleration of the body motion on an inclined plane.
10. Euclid 5
Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm.
11. Diagonal
Can a rhombus have the same length diagonal and side?
12. Clouds
From two points A and B on the horizontal plane was observed forehead cloud above the two points under elevation angle 73°20' and 64°40'. Points A , B are separated by 2830 m. How high is the cloud?
13. Climb
For horizontal distance 4.2 km road rise by 6.3 m. Calculate the road pitch in ‰ (permille, parts per thousand).
14. Cable car
Cable car rises at an angle 45° and connects the upper and lower station with an altitude difference of 744 m. How long is "endless" tow rope?
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?
16. 3-bracket 2
May be the smallest angle in the triangle greater than 40°?
A ship travels 84 km on a bearing of 17°, and then travels on a bearing of 107° for 135 km. Find the distance of the end of the trip from the starting point, to the nearest kilometer.
18. Angles and sides of the triangle
Triangle ABC has a circumference of 26 cm. Lengths of the sides are as follows: a = 11.2 cm; b = 6.5 cm. Arrange the interior angles in order of its size. ?
19. 7 triangle
The triangle area is 26.7 cm2. Determine the side length l if appropriate height hl = 45.3 cm.
20. Chord
Point on the circle is the end point of diameter and end point of chord length of radius. What angle between chord and diameter?

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