Question

find the exact value of tan y in simplest radical form.
(image of a right triangle xyw with right angle at x, xy = √96, xw = 10, yw = 14)
answer attempt 1 out of 2
tan y = |
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Explanation:

Step1: Identify sides for tan Y

In right triangle YXW, tan Y = opposite/adjacent to Y. Opposite: XW = 10; Adjacent: XY = √96.

Step2: Simplify the ratio

tan Y = 10/√96. Rationalize denominator: 10√96 / 96. Simplify √96 = 4√6, so 10*4√6 /96 = 40√6/96 = 5√6/12.

Answer:

$\frac{5\sqrt{6}}{12}$