# Goniomentry and trigonometry - examples - page 4

1. Rhombus
Internal angles of rhombus is in ratio 2:3. How many times is the shorter diagonal longer than side of rhombus?
2. Sphere in cone
A sphere of radius 3 cm desribe cone with minimum volume. Determine cone dimensions.
An airplane leaves an airport and flies due west 120 miles and then 150 miles in the direction S 44.1°W. How far is the plane from the airport (round to the nearest mile)?
4. Water inlets
Inlet valve with a flow rate of 12 liters per second is filled tank for 72 minutes. How long take to fill full tank if we open one more such valve half an hour after?
5. House roof
The roof of the house has the shape of a regular quadrangular pyramid with a base edge 17 m. How many m2 is needed to cover roof if roof pitch is 57° and we calculate 11% of waste, connections and overlapping of area roof?
6. V-belt
Calculate the length of the belt on pulleys with diameters of 105 mm and 393 mm at shaft distance 697 mm.
7. Pentagonal pyramid
Calculate the volume of a regular 5-side (pentaprism) pyramid ABCDEV; if |AB| = 7.7 cm and a plane ABV, ABC has angle 37 degrees.
8. Triangle in circle
Vertices of the triangle ABC lies on a circle with radius 3 so that it is divided into three parts in the ratio 4:4:4. Calculate the circumference of the triangle ABC.
9. Trigonometry
If you know that cos(γ) = sin (806°), what is the angle γ?
10. Q-Exam
If tg α = 0.9, Calculating sin α, cos α, cotg α .
11. EQL triangle
12. Block
Calculate the volume of a cuboid ABCDEFGH if |AB| = 16 cm, |BC| = 19 cm and the angle ∠CDG = 36.9°
13. Geodesist
Triangle shaped field (triangle ABC) has side AB = 129 m. path XY is parallel to the side AB which divided triangle ABC into two parts with same area. What will be the length of the path XY? Help please geodesist ...
14. Tractors
Six tractors plowing the field for 8 days. After two days, two tractors broke down. How many days were prolonged work in the field?
15. Slope of the pool
Calculate slope (rise:run) of the bottom of swimming pool long 10 m. Water depth at beginning of pool is 1.16 m (for children) and depth at end is 1.89 m (for swimmers). Slope express as percentage and as angle in degrees.
16. Shooter
The shooter fired to a target from distance 11 m The individual concentric circle of targets have a radius increments 1 cm (25 points) by 1 point. Shot was shifted by 8'(angle degree minutes). How many points should win his shot?
17. Nine-gon
Calculate the perimeter of a regular nonagon (9-gon) inscribed in a circle with a radius 13 cm.
18. Side c
In △ABC a=2, b=4 and ∠C=100°. Calculate length of the side c.
19. Black building
Keith built building with a rectangular shape 6.5 m × 3.9 m. Calculate how much percent exceeded the limit 25 m2 for small building. Building not built in accordance with the law is called "black building". Calculate the angle that the walls were clenchin