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msm555

Answer:

tan V = 3.43

Step-by-step explanation:

To solve for [tex]\bold{\sf \tan V }[/tex] in triangle [tex]\bold{\sf TUV }[/tex], we can use trigonometric ratios in a right triangle.

Given:

  • [tex]\bold{\sf U = 90^\circ }[/tex] (angle at vertex [tex]\bold{\sf U }[/tex] is a right angle)
  • [tex]\bold{\sf TV = 50 }[/tex] (length of hypotenuse)
  • [tex]\bold{\sf UV = 14 }[/tex] (length of adjacent side)
  • [tex]\bold{\sf TU = 48 }[/tex] (length of opposite side)

We can use the definition of tangent ([tex]\bold{\sf \tan }[/tex]) in a right triangle:

[tex]\large\boxed{\boxed{\sf \tan V = \dfrac{\textsf{opposite}}{\textsf{adjacent}}}} [/tex]

In triangle [tex]\bold{\sf TUV }[/tex], [tex]\bold{\sf V }[/tex] is the acute angle opposite the side [tex]\bold{\sf TU }[/tex] (the opposite side) and adjacent to the side [tex]\bold{\sf UV }[/tex] (the adjacent side).

Identify the opposite and adjacent sides:

  •    Opposite side ([tex]\bold{\sf TU }[/tex]) = 48
  •    Adjacent side ([tex]\bold{\sf UV }[/tex]) = 14

Apply the tangent ratio:

  [tex]\sf \tan V = \dfrac{TU}{UV} [/tex]

  [tex]\sf \tan V = \dfrac{48}{14} [/tex]

Simplify the tangent ratio:

  [tex]\sf \tan V = \dfrac{48}{14} [/tex]

  [tex]\sf \tan V  = 3.4285714285714 [/tex]

  [tex]\sf \tan V =3.43 \textsf{ (in nearest hundredth)}[/tex]

Therefore, [tex]\bold{\sf \tan V }[/tex] is approximately [tex]\bold{\sf \boxed{3.43} }[/tex].

semsee45

Answer:

3.43

Step-by-step explanation:

The tangent ratio of an angle in a right triangle is the ratio of the side opposite of the angle to the side adjacent to the angle.

[tex]\boxed{\begin{array}{l}\underline{\textsf{Tangent trigonometric ratio}}\\\\\sf \tan(\theta)=\dfrac{O}{A}\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$\theta$ is the angle.}\\\phantom{ww}\bullet\;\textsf{$O$ is the side opposite the angle.}\\\phantom{ww}\bullet\;\textsf{$A$ is the side adjacent the angle.}\end{array}}[/tex]

In this case:

  • θ = V
  • O = UT = 48
  • A = UV = 14

Substitute the values into the ratio and solve for tan V:

[tex]\tan V=\dfrac{48}{14}\\\\\\\tan V=3.42857142857...\\\\\\\tan V=3.43\; \sf (nearest\;tenth)[/tex]

Therefore, the value of tan V rounded to the nearest hundredth is:

[tex]\Large\text{$\tan V=\boxed{3.43}$}[/tex]

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