Question

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Answer 1

The trigonometric function gives the ratio of different sides of a right-angle triangle. The area of the triangle is 55.4256 ft².

What are Trigonometric functions?

The trigonometric function gives the ratio of different sides of a right-angle triangle.

$\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}$

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.

For the given triangle the length of AB and BC can be written as,

$\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Sin(30^o) = \dfrac{AB}{AC}\\\\\\AB = Sin(30^o) \times 16 \\\\\\AB=8\rm\ ft$

$Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Cos(30^o) = \dfrac{BC}{AC}\\\\\\BC = Cos(30^o) \times AC\\\\\\BC = 13.8564\rm\ ft$

Now, the area of the triangle is,

Area of triangle = 0.5× 8 × 13.8564 = 55.4256 ft²

Hence, the area of the triangle is 55.4256 ft².

Learn more about Trigonometric functions:

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