Trigonometric function is the ratio of the different sides of the triangle. The correct value of Tanθ is 7/5.
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}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/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.
We know that the value of the perpendicular height of the cone is 7 inches while the measurement of the base of the triangle is 5 inches, therefore, using Pythagoras theorem the third side of the triangle can be written as,
[tex]\rm(Slant\ Height)^2 = 7^2 + 5^2\\\\(Slant\ Height)^2 =49+25\\\\(Slant\ Height)= 8.6[/tex]
Now, the value of the trigonometric ratios can be written as,
[tex]\rm Sin \theta=\dfrac{7}{8.6}\\\\\\Cos \theta=\dfrac{5}{8.6}\\\\\\Tan \theta=\dfrac{7}{5}\\\\\\Cosec \theta=\dfrac{8.6}{7}\\\\\\Sec \theta=\dfrac{8.6}{5}\\\\\\Cot \theta=\dfrac{5}{7}\\\\\\[/tex]
Hence, the correct value of Tanθ is 7/5.
Learn more about Trigonometric functions:
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