Cosine - problems - page 4

1. 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?
2. Ball
Ball was fired at an angle of 35° at initial velocity 437 m/s. Determine the length of the litter. (g = 9.81 m/s2).
3. Cosine
The point (8, 6) is on the terminal side of angle θ. cos θ = ?
4. Chord MN
Chord MN of circle has distance from the center circle S 120 cm. Angle MSN is 64°. Determine the radius of the circle.
5. Height of the arc - formula
Calculate the height of the arc if the length of the arc is 77 and chord length 40. Does exist a formula to solve this?
6. Right triangle trigonometrics
Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60° and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent)
7. Three vectors
The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point so that they are in balance. Determine the angles of the each two forces.
8. Four sides of trapezoid
In the trapezoid ABCD is |AB| = 73.6 mm; |BC| = 57 mm; |CD| = 60 mm; |AD| = 58.6 mm. Calculate the size of its interior angles.
9. Right triangle
It is given a right triangle angle alpha of 90 degrees beta angle of 55 degrees c = 10 cm use Pythagorean theorem to calculate sides a and b
10. Bearing
A plane flew 50 km on a bearing 63°20' and the flew on a bearing 153°20' for 140km. Find the distance between the starting point and the ending point.
11. Scalar dot product
Calculate u.v if |u| = 5, |v| = 2 and when angle between the vectors u, v is: a) 60° b) 45° c) 120°
12. The mast
A 40 m high mast is secured in half by eight ropes of 25 m long. The ends of the ropes are equidistant from each other. Calculate this distance.
13. Triangle ABC v2
Area of the triangle is 12 cm square. Angle ACB = 30º , AC = (x + 2) cm, BC = x cm. Calculate the value of x.
14. 30-gon
At a regular 30-gon the radius of the inscribed circle is 15cm. Find the "a" side size, circle radius "R", circumference, and content area.
15. Tree
Between points A and B is 50m. From A we see a tree at an angle 18°. From point B we see the tree in three times bigger angle. How tall is a tree?
16. Forces
Forces with magnitudes F1 = 42N and F2 = 35N act at a common point and make an angle of 77°12'. How big is their resultant?
17. Cylinder horizontally
The cylinder with a diameter of 3 m and a height/length of 15 m is laid horizontally. Water is poured into it, reaching a height of 60 cm below the axis of the cylinder. How many hectoliters of water is in the cylinder?
18. Hot air balloon
The center of the balloon is at an altitude of 600 m above the ground (AGL). From habitat on earth is the center of the balloon to see in elevation angle 38°20' and the balloon is seen from the perspective of angle 1°16'. Calculate the diameter of the bal
19. Inner angles
The inner angles of the triangle are 30°, 45° and 105° and its longest side is 10 cm. Calculate the length of the shortest side, write the result in cm up to two decimal places.
20. Regular n-gon
Which regular polygon have a radius of circumscribed circle r = 10 cm and the radius of inscribed circle p = 9.962 cm?

Do you have an interesting mathematical problem that you can't solve it? Enter it, and we can try to solve it.

To this e-mail address, we will reply solution; solved examples are also published here. Please enter e-mail correctly and check whether you don't have a full mailbox.