The trigonometric function gives the ratio of different sides of a right-angle triangle. The value of x is 2.3 cm.
What are Trigonometric functions?
The trigonometric function gives the ratio of different sides of a right-angle triangle.
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.
The triangle with the x will match with the fourth triangle, therefore, using the cosine function the ratio of the two given triangles can be written as,
Cosine(55°) = Base/Hypotenuse = 0.57/1 = x/4
0.57/1 = x/4
x = 0.57 × 4
x = 2.2943 ≈ 2.3
Hence, the value of x is 2.3 cm.
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