Question

Find the tangent of ∠T. for the triangle
48 bottom
55 left side (straight)
73 right side (slanted)
T bottom right corner
V bottom left corner
U top of triangle
Simplify your answer and write it as a proper fraction, improper fraction, or whole number.
tan(T)=

Answer 1

In triangle \( UVT \), where \( UV = 55 \) (left side), \( UT = 48 \) (bottom), and \( VT = 73 \) (right side), we want to find the tangent of angle \( T \).

To find \( \tan(T) \), we use the definition of tangent in a right triangle:

\[
\tan(T) = \frac{\text{opposite}}{\text{adjacent}}
\]

In this triangle, angle \( T \) is opposite side \( UV \) (which is 55) and adjacent to side \( UT \) (which is 48). Therefore, we have:

\[
\tan(T) = \frac{UV}{UT} = \frac{55}{48}
\]

Thus, the tangent of angle \( T \) is:

\[
\tan(T) = \frac{55}{48}
\]

This fraction is already in its simplest form, so the final answer is:

\[
\boxed{\frac{55}{48}}
\]