Answer:
[tex] \sf \tan(T) =\dfrac{{15}}{{8}}[/tex]
Step-by-step explanation:
Given:
In ∆ UVT
- Opposite (UV) = 15
- Hypotenuse (UT) = 17
To find:
Solution:
To find the tangent of ∠ T in triangle ∆ UVT, we use the definition of tangent:
[tex] \Large \boxed{\boxed{\sf \tan(T) =\dfrac{{\textsf{Opposite}}}{{\textsf{Adjacent}}}}}[/tex]
[tex] \sf \tan(T) =\dfrac{{\textsf{UV}}}{{\textsf{VT}}} [/tex]
We need to find the length of the adjacent side (VT) using the Pythagorean theorem:
[tex] \sf UT^2 = UV^2 + VT^2[/tex]
[tex] \sf 17^2 = 15^2 + VT^2[/tex]
[tex] \sf 289 = 225 + VT^2[/tex]
[tex] \sf VT^2 = 289 - 225[/tex]
[tex] \sf VT^2 = 64[/tex]
[tex] \sf VT = \sqrt{64}[/tex]
[tex] \sf VT = 8[/tex]
Now, substitute the values into the formula for tangent:
[tex] \sf \tan(T) =\dfrac{{15}}{{8}}[/tex]
So, the tangent of ∠ T is 15/8.
