Answer:
CD = 3/√2 in
Explanation:
You want the measure of altitude CD in isosceles right triangle ACB with the right angle at C.
Similar triangles
All of the isosceles right triangles in this figure are similar, and all have sides in the ratio 1 : 1 : √2.
In ∆BCD, side BC is the longest, given as 3 in. That means the other two sides of that triangle are ...
CD = BD = CB/√2
CD = 3/√2 in
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Additional comment
Often, we like to rationalize the denominator of expressions involving roots. That would make the expression for CD be ...
CD = 3/√2 = (3/2)√2 = 1.5√2
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