Question

identifying trig ratios (diagram), level 1
score: 3/10 penalty: none
question
express $\tan u$ as a fraction in simplest terms.
answer attempt 1 out of 2
$\tan u=$ submit answer

Explanation:

Step1: Find the length of \( UT \) using Pythagoras' theorem

In right - triangle \( \triangle TUS \), by Pythagoras' theorem \( a^{2}+b^{2}=c^{2} \), where \( c = 20 \) (hypotenuse) and \( b = 16 \). Let \( a=UT \). Then \( UT=\sqrt{20^{2}-16^{2}}=\sqrt{(20 + 16)(20 - 16)}=\sqrt{36\times4}=\sqrt{144}=12 \).

Step2: Recall the definition of the tangent ratio

The tangent of an angle in a right - triangle is defined as \( \tan\theta=\frac{\text{opposite}}{\text{adjacent}} \). For \( \angle U \), the opposite side to \( \angle U \) is \( TS = 16 \) and the adjacent side is \( UT = 12 \).

Answer:

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