# Goniomentry and trigonometry - examples - page 12

1. Right triangle eq2
Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
2. Working time
At 10 hours work shift, work is done in 16 days. How many days will the work be done at 8 hours shifts?
3. Proportion
write the following proportion 8 is to 64 as to 2 is to x
4. Study
For 7 hours study, she scored a 75 so if she made 93 how many hours would she need to study?
5. Pumps
After the floods, four equally powerful pumps exhausted water from the flooded cellar in 6 hours. How many hours would take a drained out with three equally powerful pumps?
6. ABCD
AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD
7. Cuboids
Two separate cuboids with different orientation in space. Determine the angle between them, knowing the direction cosine matrix for each separate cuboid. u1=(0.62955056, 0.094432584, 0.77119944) u2=(0.14484653, 0.9208101, 0.36211633)
8. Ratios
Reduce the numbers: 50 in a 1:2 ratio 111 at a ratio of 2:3 70 at 10:50 560 at a ratio of 3:8
9. Trapezoid - intersection of diagonals
In the ABCD trapezoid is AB = 8 cm long, trapezium height 6 cm, and distance of diagonals intersection from AB is 4 cm. Calculate trapezoid area.
10. How far
From the top of a lighthouse 145 ft above sea level, the angle of depression of a boat 29°. How far is the boat from the lighthouse?
11. Five pumps
The water tank is filled with two pumps in 48 minutes. How long would it take to fill it with 5 same pumps?
12. Bicycle gears
The toothed wheel on the bicycle pedal has 40 teeth, the wheel on the rear wheel has only 16 teeth. How many times does the rear wheel turn if the pedals rotate 50 times?
The angle of a straight road is approximately 12 degrees. Determine the percentage of this road.
14. Two forces
The two forces F1 = 580N and F2 = 630N have the angle of 59 degrees. Calculate their resultant force F.
15. Clouds
Approximately at what height is the cloud we see under an angle of 26°10' and see the Sun at an angle of 29°15' and the shade of the cloud is 92 meters away from us?
16. Two brothers
The two brothers were to be divided according to the will of land at an area of 1ha 86a 30m2 in a ratio of 5:4. How many will everyone get?
17. Five mechanics
Five mechanics will make a car for some time. How many cars can 30 mechanics produce at the same time?
If we read the book at a speed of 15 pages a day, we read it 3 days before we read it at a speed of 10 pages per day. If I read at 6 pages per day, how many days will I read the book?
19. Decagon
Calculate the area and circumference of the regular decagon when its radius of a circle circumscribing is R = 1m