Question

find the exact value of tan a in simplest radical form.
answer attempt 1 out of 3

Explanation:

Step1: Recall the definition of tangent in a right triangle

In a right triangle, the tangent of an acute angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. For angle \( A \) in right triangle \( ABC \) (right - angled at \( C \)):
\(\tan A=\frac{\text{opposite side to }A}{\text{adjacent side to }A}\)

Step2: Identify the opposite and adjacent sides to angle \( A \)

• The side opposite to angle \( A \) is \( BC \), and from the diagram, \( BC = 7 \).
• The side adjacent to angle \( A \) is \( AC \), and from the diagram, \( AC=6 \).

Step3: Calculate \(\tan A\)

Using the formula for tangent, we substitute the lengths of the opposite and adjacent sides:
\(\tan A=\frac{BC}{AC}=\frac{7}{6}\)

Answer:

\(\frac{7}{6}\)