# Goniomentry and trigonometry - examples - page 14

1. Two bricks One brick weighs 1kg and half a brick, how many weigh two bricks?
2. The mast The top of the pole we see at an angle of 45°. If we approach the pole by 10 m, we see the top of the pole at an angle of 60°. What is the height of the pole?
3. If the If the tangent of an angle of a right angled triangle is 0.8. Then its longest side is. .. .
4. Pilot How high is the airplane's pilot to see 0.001 of Earth's surface?
5. Diagonals of pentagon Calculate the diagonal length of the regular pentagon: a) inscribed in a circle of radius 12dm; b) a circumscribed circle with a radius of 12dm.
6. Mast shadow Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 15°. Determine the height of the mast, if the sun above the horizon is at angle 33°. Use the law of sines.
7. SSA and geometry The distance between the points P and Q was 356 m measured in the terrain. The PQ line can be seen from the viewer at a viewing angle of 107° 22 '. The observer's distance from P is 271 m. Determine the viewing angle of P and observer.
8. Right triangle Ladder 16 feet reaches up 14 feet on a house wall. The 90-degree angle at the base of the house and wall. What are the other two angles or the length of the leg of the yard?
9. Depth angle From a cliff of 150 meters high, we can see the ship at a depth angle of 9° at sea. How far is the ship from the cliff?
10. An angle An angle x is opposite side AB which is 10, and side AC is 15 which is hypotenuse side in triangle ABC. Calculate angle x.
11. Hexagon ABCDEF In the regular hexagon ABCDEF, the diagonal AE has a length 8cm. Calculate the circumference and the hexagon area.
12. KLM triangle Find the length of the sides of the triangle KLM if m = 5cm height to m = 4.5 cm and size MKL angle is 70 degrees.
13. A boy A boy of height 1.7m is standing 30m away from flag staff on the same level ground . He observes that the angle of deviation of the top of flag staff is 30 degree. Calculate the height of flag staff.
14. Ditch Ditch profile is an isosceles trapezoid with bases of length 80m and 60m. The slope of the side wall of the ditch is 80°. Calculate the ditch depth.
15. Balloon and bridge From the balloon, which is 92 m above the bridge, one end of the bridge is seen at a depth angle of 37° and the second end at depth angle 30° 30 '. Calculate the length of the bridge.
16. Calculate 2 Calculate the largest angle of the triangle whose side are 5.2cm, 3.6cm, and 2.1cm
17. Earth's circumference Calculate the Earth's circumference of the parallel 48 degrees and 10 minutes.
18. Substitution method Solve goniometric equation: sin4 θ - 1/cos2 θ=cos2 θ - 2
19. Proportion 2 A car is able to travel 210 km in 3 hours. How far can it travel in 5 hours? Put what kind of proportion is this and show your solution.
20. Two boats Two boats are located from a height of 150m above the surface of the lake at depth angles of 57° and 39°. Read the distance of both boats if the sighting device and both ships are in a plane perpendicular to the surface of the lake.

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Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.