Question

identifying trig ratios (no diagram)
question
in \\( \delta \mathrm{stu} \\), the measure of \\( \angle \mathrm{u}=90^{\circ}, \mathrm{ut}=4 \\), \\( \mathrm{ts}=5 \\), and \\( \mathrm{su}=3 \\). what is the value of the tangent of \\( \angle \mathrm{t} \\) to the nearest hundredth?
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Explanation:

Step1: Recall the tangent ratio formula

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). For \(\angle T\), the side opposite to \(\angle T\) is \(SU\) and the side adjacent to \(\angle T\) is \(UT\).

Step2: Substitute the values into the formula

We know that \(SU = 3\) and \(UT=4\). So, \(\tan T=\frac{SU}{UT}\).
Substituting the values, we get \(\tan T=\frac{3}{4}=0.75\)

Answer:

\(0.75\)