Question

in δuvw, the measure of ∠w = 90°, vu = 37, wv = 35, and uw = 12. what is the value of the tangent of ∠v to the nearest hundredth?

Explanation:

Step1: Recall the tangent formula

In a right - triangle, for an angle \(\theta\), \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). For \(\angle V\) in right - triangle \(UVW\) with \(\angle W = 90^{\circ}\), the side opposite to \(\angle V\) is \(UW\) and the side adjacent to \(\angle V\) is \(WV\).

Step2: Substitute the values into the formula

We know that \(UW = 12\) and \(WV=35\). Then \(\tan V=\frac{UW}{WV}\).
Substitute \(UW = 12\) and \(WV = 35\) into the formula: \(\tan V=\frac{12}{35}\).

Step3: Calculate the value

\(\frac{12}{35}\approx0.34\) (using a calculator: \(12\div35 = 0.342857\cdots\))

Answer:

\(0.34\)