Application: Finding The Angle of A Right Triangle
Inverse trigonometric functions are useful when trying to determine the remaining two angles of a right triangle when the lengths of the sides of the triangle are known. Recalling the right-triangle definitions of sine, for example, it follows that
Often, the hypotenuse is unknown and would need to be calculated before using arcsine or arccosine using the Pythagorean Theorem: where is the length of the hypotenuse. Arctangent comes in handy in this situation, as the length of the hypotenuse is not needed.
For example, suppose a roof drops 8 feet as it runs out 20 feet. The roof makes an angle θ with the horizontal, where θ may be computed as follows:
Read more about this topic: Inverse Trigonometric Functions
Famous quotes containing the words finding and/or angle:
“It must
Be the finding of a satisfaction, and may
Be of a man skating, a woman dancing, a woman
Combing. The poem of the act of the mind.”
—Wallace Stevens (1879–1955)
“The good lawyer is not the man who has an eye to every side and angle of contingency, and qualifies all his qualifications, but who throws himself on your part so heartily, that he can get you out of a scrape.”
—Ralph Waldo Emerson (1803–1882)