Expression of a variable from the formula + The Law of Cosines - math problems

Number of problems found: 19

Two forces 3
Two forces of magnitude 8 Newtons and 15 Newtons respectively act at a point. If the resultant force is 17 Newtons, find the angle between the forces.
Calculate triangle
In the triangle ABC, calculate the sizes of all heights, angles, perimeters and its area, if given a-40cm, b-57cm, c-59cm
The farmer
The farmer sees the back fence of the land, which is 50 m long at a viewing angle of 30 degrees. It is 92 m away from one end of the fence. How far is it from the other end of the fence?
Triangle's centroid
In the triangle ABC the given lengths of its medians tc = 9, ta = 6. Let T be the intersection of the medians (triangle's centroid) and point is S the center of the side BC. The magnitude of the CTS angle is 60°. Calculate the length of the BC side to 2 d
Distance of points
A regular quadrilateral pyramid ABCDV is given, in which edge AB = a = 4 cm and height v = 8 cm. Let S be the center of the CV. Find the distance of points A and S.
Quadrilateral oblique prism
What is the volume of a quadrilateral oblique prism with base edges of length a = 1m, b = 1.1m, c = 1.2m, d = 0.7m, if a side edge of length h = 3.9m has a deviation from the base of 20° 35' and the edges a, b form an angle of 50.5°.
Two chords
From the point on the circle with a diameter of 8 cm, two identical chords are led, which form an angle of 60°. Calculate the length of these chords.
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?
Triangle from median
Calculate the perimeter, content, and magnitudes of the triangle ABC's remaining angles, given: a = 8.4; β = 105° 35 '; and median ta = 12.5.
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 ’?
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 a
Circular railway
The railway connects in a circular arc the points A, B, and C, whose distances are | AB | = 30 km, AC = 95 km, BC | = 70 km. How long will the track from A to C?
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.
Parallelogram
The sides of the parallelogram are 8 cm and 6 cm long, and the diagonals' angle is 60°. What is its area?
Children playground
The playground has a trapezoid shape, and the parallel sides have a length of 36 m and 21 m. The remaining two sides are 14 m long and 16 m long. Find the size of the inner trapezoid angles.
Calculate 2
Calculate the largest angle of the triangle whose side are 5.2cm, 3.6cm, and 2.1cm
The pond
We can see the pond at an angle 65°37'. Its end points are 155 m and 177 m away from the observer. What is the width of the pond?
Largest angle of the triangle
Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a
Heron backlaw
Calculate missing side in a triangle with sides 25 and 13 and area 152.