In the figure above, \( \tan B = \frac{3}{2} \). If \( BC = 15 \) and \( DA = 4 \), what is the length of...
In the figure above, \( \tan B = \frac{3}{2} \). If \( BC = 15 \) and \( DA = 4 \), what is the length of \( DE \)?
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info@snapandsolve.comGiven that \( \tan B = \frac{3}{2} \), we know that \( \tan B = \frac{\text{opposite}}{\text{adjacent}} \). Therefore, if \( BC = 15 \), then \( AB = \frac{2}{3} \times 15 = 10 \).
Since \( DA = 4 \), triangle \( ADE \) is similar to triangle \( ABC \) by AA similarity (both have a right angle and share angle \( A \)).
The ratio of similarity is \( \frac{AD}{AB} = \frac{4}{10} = \frac{2}{5} \).
Thus, \( DE = \frac{2}{5} \times BC = \frac{2}{5} \times 15 = 6 \).
The length of \( DE \) is 6.
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