find the tangent of $angle t$.\nsimplify your answer and write it as a proper fraction, improper fraction…

find the tangent of $angle t$.\nsimplify your answer and write it as a proper fraction, improper fraction, or whole number.\n$\tan(t) = square$

find the tangent of $angle t$.\nsimplify your answer and write it as a proper fraction, improper fraction, or whole number.\n$\tan(t) = square$

Answer

Answer:

$\frac{5}{12}$

Explanation:

Step1: Recall tangent definition

For an acute angle in a right triangle, $\tan(\theta) = \frac{\text{opposite side}}{\text{adjacent side}}$.

Step2: Identify similar triangles

$\triangle TRU \sim \triangle TSV$, so the ratio of opposite to adjacent for $\angle T$ is equal to $\frac{RV}{SV} = \frac{35}{84}$.

Step3: Simplify the fraction

Divide numerator and denominator by 7: $\frac{35\div7}{84\div7} = \frac{5}{12}$