Nate Y. answered • 01/14/20
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This is a trigonometry problem that you can do with SOH CAH TOA.
In a right triangle, from the perspective of the angle Θ, there are two shorter sides (legs). The one next to Θ is called the adjacent side and the one that is directly across from Θ is called the opposite side. The long side that is across from the 90 degree right angle is called the hypotenuse.
The definition of the sine of Θ in a right triangle is the ratio of the opposite side divided by the hypotenuse. That's why we say "SOH" to remember that sine is the opposite / hypotenuse.
Cosine of Θ is the adjacent side divided by the hypotenuse- adjacent / hypotenuse for cosine is abbreviated CAH.
The third basic trigonometric identity is tangent of Θ, which is the ratio of opposite / adjacent (TOA).
In this question, you can see that the ratio of O/H is √23/12 and the ratio of O/A is √23/11.
These two facts tell you the proportion of Opposite to Hypotenuse to Adjacent. You could imagine this as a triangle with our angle Θ, and the opposite side is √23, the adjacent side is 11, and the hypotenuse is 12.
Given what you now know about the cosine ratio for Θ and the possible sides of its triangle, how can you find its value?
