Question

identifying trig ratios (diagram), level 1
score: 8/10 penalty: none
question
find the value of tan u rounded to the nearest hundredth, if necessary.
answer
attempt 1 out of 2
tan u =

Explanation:

Step1: Find the length of \( ST \)

Use the Pythagorean theorem \( a^{2}+b^{2}=c^{2} \). Here \( c = 5 \), \( b = 3 \), and \( a=ST \).

$$
LATEXBLOCK0
$$

Step2: Calculate \( \tan U \)

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 is \( ST = 4 \) and the adjacent side is \( UT=3 \).

$$ \tan U=\frac{ST}{UT}=\frac{4}{3}\approx1.33 $$

Answer:

\( 1.33 \)