Score: $$ 6 / 8 $$ Penalty: none Question In $$ riangle \mathrm{UVW} $$, the measure of $$ \angle \mathrm{W}=90^{\circ}, \mathrm{VU}=37 $$, $$ \mathrm{WV}=35 $$, and $$ \mathrm{UW}=12 $$. What is the value of the tangent of $$ \angle \mathrm{V} $$ to the nearest hundredth?

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Score: $$ 6 / 8 $$ Penalty: none Question In $$ 	riangle \mathrm{UVW} $$, the measure of $$ \angle \mathrm{W}=90^{\circ}, \mathrm{VU}=37 $$, $$ \mathrm{WV}=35 $$, and $$ \mathrm{UW}=12 $$. What is the value of the tangent of $$ \angle \mathrm{V} $$ to the nearest hundredth?

UpStudy AI · Accepted Answer

To find the tangent of $$ \angle V $$ in the right triangle $$ \triangle UVW $$ with the right angle at $$ W $$, follow these steps:

1. **Identify the Sides:**
   - **Hypotenuse (opposite the right angle $$ W $$)**: $$ UV = 37 $$
   - **Adjacent side to $$ \angle V $$**: $$ VW = 35 $$
   - **Opposite side to $$ \angle V $$**: $$ UW = 12 $$

2. **Calculate the Tangent:**
   The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side.

$$
   \tan V = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{UW}{VW} = \frac{12}{35}
   $$

3. **Compute the Value:**
   
   $$
   \frac{12}{35} \approx 0.342857
   $$

4. **Round to the Nearest Hundredth:**
   
   $$
   0.342857 \approx 0.34
   $$

**Answer:**  
The tangent of $$ \angle V $$ is $$ 0.34 $$.
The tangent of $$ \angle V $$ is $$ 0.34 $$.

Score: \( 6 / 8 \) Penalty: none Question In \( \triangle \mathrm{UVW} \), the measure of \( \angle \mathrm{W}=90^{\circ}, \mathrm{VU}=37 \), \( \mathrm{WV}=35 \), and \( \mathrm{UW}=12 \). What is the value of the tangent of \( \angle \mathrm{V} \) to the nearest hundredth?

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