find tv.\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\ntv =
find tv.\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\ntv =
Answer
Explanation:
Step1: Identify the trigonometric ratio
In right - triangle ( \triangle UVT), we know the side (UV = 7) (opposite side to angle (T)) and we want to find (TV) (adjacent side to angle (T)). The trigonometric ratio that relates the opposite and adjacent sides of a right - triangle is the tangent ratio. The formula for the tangent of an angle in a right - triangle is (\tan\theta=\frac{\text{opposite}}{\text{adjacent}}). Here, (\theta = 67^{\circ}), the opposite side (opp = UV = 7), and the adjacent side (adj=TV). So, (\tan(67^{\circ})=\frac{UV}{TV}).
Step2: Solve for (TV)
We can rewrite the formula (\tan(67^{\circ})=\frac{7}{TV}) as (TV=\frac{7}{\tan(67^{\circ})}). We know that (\tan(67^{\circ})\approx2.356). Then (TV=\frac{7}{2.356}\approx3.0).
Answer:
(3.0)