# Right triangle - 8th grade (13y) - examples - page 10

1. 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?
2. Climb For horizontal distance 4.2 km road rise by 6.3 m. Calculate the road pitch in ‰ (permille, parts per thousand).
3. Rhombus IV Calculate the length of the diagonals of the rhombus, whose lengths are in the ratio 1: 2 and a rhombus side is 35 cm.
4. Distance Wha is the distance between the origin and the point (18; 22)?
5. Journey Charles and Eva stands in front of his house, Charles went to school south at speed 5.4 km/h, Eva went to the store on a bicycle eastwards at speed 21.6 km/h. How far apart they are after 10 minutes?
6. Acreage What acreage has a rectangular plot whose diagonal is 34 meters long and one side has a length of 16 meters. ?
7. 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?
8. Bevel I have bevel in the ratio 1:6. What is the angle and how do I calculate it?
9. Tetrahedral pyramid It is given a regular tetrahedral pyramid with base edge 6 cm and the height of the pyramid 10 cm. Calculate the length of its side edges.
10. Parallelogram +ľ | AB | = 76cm, | BC | = 44cm, angle BAD = 30 °. Find the area of the parallelogram.
11. Concentric circles In the circle with diameter 19 cm is constructed chord 9 cm long. Calculate the radius of a concentric circle that touches this chord.
12. Acute angles Sizes of acute angles in the right-angled triangle are in the ratio 1: 3. What is size of the larger of them?
13. 6 regular polygon It is given 6 side regular polygon whose side is 5 cm. Calculate its content area. Compare how many more cm2 (square centimeters) has a circle in which is inscribed the 6-gon.
14. Lamp cone Calculate the surface of a lamp shade shaped of a rotary truncated cone with base diameter 32 cm and 12 cm and height 24 cm.
15. Median In triangle ABC is given side a=10 cm and median ta= 13 cm and angle gamma 90°. Calculate length of the median tb.
16. Cosine The point (8, 6) is on the terminal side of angle θ. cos θ = ?
17. Tree How tall is the tree that observed in the visual angle of 52°? If I stand 5 m from the tree and eyes are two meters above the ground.
18. Rhombus ABCD is a rhombus, ABD is an equilateral triangle and AC is equal to 4. Find the area of the rhombus. 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? Right triangle ABC with side a = 19 and the area S = 95. Calculate the length of the remaining sides.