A trapezoid

A trapezoid with a base length of a = 36.6 cm, with angles α = 60°, β = 48°, and the height of the trapezoid is 20 cm. Calculate the lengths of the other sides of the trapezoid.

Correct answer:

b =  23.094 cm
d =  26.9127 cm
c =  5.1356 cm

Step-by-step explanation:

a=36.6 cm α=60  β=48   h=20 cm  sin α = h:b  b=h/sin(α)=20/sin(60°)=23.094 cm
sin β = h:d  d=h/sin(β)=20/sin(48°)=26.9127 cm
x1+c+x2 = a cosα=x1:d=x1:26.9127=0=0:1 cosβ=x2:d=x2:26.9127=0=0:1  c=ad (cosα+cosβ)=ad (cos60° +cos48° )=36.626.9127 (cos60° +cos48° )=36.626.9127 (0.5+0.669131)=5.136=5.1356 cm

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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.

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