Question

express tan u as a fraction in simplest terms.
answer attempt 1 out of 2
tan u =

Explanation:

Step1: Find the length of \( UT \)

Use the Pythagorean theorem \( a^{2}+b^{2}=c^{2} \). Let \( a = UT \), \( b = 16 \), \( c = 20 \). Then \( a=\sqrt{20^{2}-16^{2}}=\sqrt{(20 + 16)(20 - 16)}=\sqrt{36\times4}=\sqrt{144}=12 \).

Step2: Calculate \( \tan U \)

By the definition of tangent in a right - triangle \( \tan\theta=\frac{\text{opposite}}{\text{adjacent}} \). For \( \angle U \), the opposite side to \( \angle U \) is \( TS = 16 \) and the adjacent side is \( UT=12 \). So \( \tan U=\frac{16}{12}=\frac{4}{3} \).

Answer:

\(\frac{4}{3}\)