Using Trig. Ratios to Find Distances – Practice ProblemsHaving fun while studying, practice your skills by solving these exercises!

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When learning about the law of sines and cosines, it is important to remember the Pythagorean Theorem: c2 = a2 + b2, and the trigonometric ratios; specifically, sine and cosine.

The law of sines and cosines is another tool for finding unknown angles and side lengths of triangles. This law was derived from the Pythagorean Theorem and trigonometric ratios and is stated as follows:

Law of Sines:

a b c
------ = ------ = ------
sinA sinB sinC

Law of Cosines:

c2 = a2 + b2 – 2ab(cosC)
b2 = a2 + c2 – 2ac(cosB)
a2 = b2 + c2 – 2bc(cosA)

where the lower case a,b and ,c are the lengths of the sides of the triangle and upper case A, B, and C
are the measurement of the angles.

This video provides examples and shows how to use the law of sines and cosines to find angles and side lengths of a triangle.

The law of sines and cosines can also be be used to find the distance of two objects. For example, if you want to find the distance between two ships in the sea from a light house, you can compute their distance once you know the length of the light beams from the lighthouse to the ships, and the angle connecting the beams.

Apply trigonometry to general triangles.

CCSS.MATH.CONTENT.HSG.SRT.D.10

Exercises in this Practice Problem
 Explain the law of cosines. Determine the height of the tree house. Calculate the height of the tree house. Figure out the length of the side $x$. Clarify the law of sines. Examine the height of the tower.