# Cosine + triangle - math problems

1. Viewing angle The observer sees a straight fence 60 m long at a viewing angle of 30°. It is 102 m away from one end of the enclosure. How far is the observer from the other end of the enclosure?
2. Triangle from median Calculate the perimeter, content, and magnitudes of the remaining angles of triangle ABC, given: a = 8.4; β = 105° 35 '; and median ta = 12.5.
3. The bases The bases of the isosceles trapezoid ABCD have lengths of 10 cm and 6 cm. Its arms form an angle α = 50˚ with a longer base. Calculate the circumference and content of the ABCD trapezoid.
4. The rescue helicopter The rescue helicopter is above the landing site at a height of 180m. The site of the rescue operation can be seen from here at a depth angle of 52° 40 '. How far will the helicopter land from the rescue site?
5. The angle of view Determine the angle of view at which the observer sees a rod 16 m long when it is 18 m from one end and 27 m from the other.
6. Two groves Two groves A, B are separated by a forest, both are visible from the hunting grove C, which is connected to both by direct roads. What will be the length of the projected road from A to B, if AC = 5004 m, BC = 2600 m and angle ABC = 53° 45 ’?
7. Decide 2 Decide whether points A[-2, -5], B[4, 3] and C[16, -1] lie on the same line
8. Angle of the body diagonals Using vector dot product calculate the angle of the body diagonals of the cube.
9. What percentage What percentage of the Earth’s surface is seen by an astronaut from a height of h = 350 km. Take the Earth as a sphere with the radius R = 6370 km
10. Power line pole From point A, the power line pole is seen at an angle of 18 degrees. From point B to which we get when going from point A 30m away from the column at an angle of 10 degrees. Find the height of the power pole.
11. Steps Find the height between the two floors if you know that the number of steps between the two floors is 18, the gradient is 30º and the length of the step is 28.6 cm. Report the result in centimeters to the nearest centimeter.
12. The spacecraft The spacecraft spotted a radar device at altitude angle alpha = 34 degrees 37 minutes and had a distance of u = 615km from Earth's observation point. Calculate the distance d of the spacecraft from Earth at the moment of observation. Earth is considered
13. Tetrahedral pyramid Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30´.
14. The aspect ratio The aspect ratio of the rectangular triangle is 13: 12: 5. Calculate the internal angles of the triangle.
15. Coordinates of square vertices I have coordinates of square vertices A / -3; 1/and B/1; 4 /. Find coordinates of vertices C and D, C 'and D'. Thanks Peter.
16. A rhombus A rhombus has sides of length 10 cm, and the angle between two adjacent sides is 76 degrees. Find the length of the longer diagonal of the rhombus.
17. Isosceles triangle 10 In an isosceles triangle, the equal sides are 2/3 of the length of the base. Determine the measure of the base angles.
18. The hemisphere The hemisphere container is filled with water. What is the radius of the container when 10 liters of water pour from it when tilted 30 degrees?
19. One side One side is 36 long with a 15° incline. What is the height at the end of that side?
20. Isosceles triangle 8 If the rate of the sides an isosceles triangle is 7:6:7, find the base angle correct to the nearest degree.

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