Question

find k.
right triangle with a right angle, one acute angle 45°, the other acute angle 45°, hypotenuse 12√2 km, one leg labeled k
write your answer in simplest radical form.
blank kilometers
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Explanation:

Step1: Identify triangle type

This is a 45 - 45 - 90 triangle (isosceles right triangle), where the hypotenuse \( h \) and leg \( l \) are related by \( h = l\sqrt{2} \).

Step2: Solve for \( k \)

Given hypotenuse \( h = 12\sqrt{2}\), and \( h = k\sqrt{2} \). So, \( k\sqrt{2}=12\sqrt{2} \). Divide both sides by \( \sqrt{2} \): \( k = \frac{12\sqrt{2}}{\sqrt{2}} = 12 \).

Answer:

12