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Digital SAT
Digital SAT Mathematics - No Calculator Section

Finding the Adjacent Side in a Trigonometric Triangle

Very Hard Additional Topics In Math Trigonometry

Consider a right triangle where one angle, $ heta$, measures 30 degrees and the length of the side opposite to this angle is 4 units. The ratio of the side opposite this angle to the hypotenuse can be expressed using the sine function:

$$ ext{sin}( heta) =\frac{ ext{opposite}}{ ext{hypotenuse}} $$

Using the information provided, determine the lengths of the other sides of the triangle. Calculate the length of the adjacent side and find the angle that corresponds to the angle in the triangle represented as:

$$ ext{adjacent} = ext{hypotenuse} imes ext{cos}(30^{ ext{o}}) $$

What is the length of the adjacent side as a decimal rounded to two decimal places?

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