# Goniometry and trigonometry - math word problems

#### Number of problems found: 336

• Forces
In point O acts three orthogonal forces: F1 = 20 N, F2 = 7 N, and F3 = 19 N. Determine the resultant of F and the angles between F and forces F1, F2, and F3.
• Diagonal
Determine the dimensions of the cuboid, if diagonal long 53 dm has an angle with one edge 42° and with another edge 64°.
• Right
Determine angles of the right triangle with the hypotenuse c and legs a, b, if: 3a +4b = 4.9c
• Climb
Road has climbing 1:27. How big is a angle corresponds to this climbing?
• Pentagon
Calculate the area of a regular pentagon, which diagonal is u=16.
• Statue
On the pedestal high 4 m is a statue 2.7 m high. At what distance from the statue must the observer stand to see it at the maximum viewing angle? Distance from the eye of the observer from the ground is 1.7 m.
• Cuboid
Find the dimensions of cuboid a, b, c; if diagonal d=9 dm has an angle with edge α=55° and has an angle with edge b β=58°
• Triangle
Calculate the area of the right triangle ΔABC if one leg is long 14 and its opposite angle is 59°.
• Angle between lines
Calculate the angle between these two lines: p: -8x +4y +5 =0 q: 10x +10y -7=0
• Mast
Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 13.3°. Determine the height of the mast, if the sun above the horizon is at angle 45°12'.
• Felix
Calculate how much land saw Felix Baumgartner after jump from 32 km above ground. The radius of the Earth is R = 6378 km.
• Arc and segment
Calculate the length of circular arc l, area of the circular arc S1 and area of circular segment S2. Radius of the circle is 11 and corresponding angle is (2)/(12) π.
• Height 2
Calculate the height of the equilateral triangle with side 27.
• Trigonometric functions
In the right triangle is: tg α= frac(2) 1 Find the value of s and c: sin α= (s)/(√ 5) cos α= (c)/(√ 5)
• Trigonometry
Is true equality? sin(x +13 π)= sin(x)
• Box
Calculate the angle between box base 9 x 14 and body diagonal length 18.
• The angle of lines
Calculate the angle of two lines y=x-21 and y=-2x+14
• V-belt
Calculate the length of the belt on pulleys with diameters of 105 mm and 393 mm at shaft distance 697 mm.
• Earth parallel
Earth's radius is 6370 km long. Calculate the length parallel of latitude 50°.
• Trigonometry
If you know that cos(γ) = sin (806°), what is the angle γ?

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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.