Question

what is the value of tan a?
6/10 or 3/5
8/10 or 4/5
8/6 or 4/3
6/8 or 3/4

Explanation:

Step1: Recall the definition of tangent in a right triangle

In a right triangle, the tangent of an acute angle is 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, \( BC = 6\space\text{cm}\).
• The side adjacent to angle \( A \) is \( AC \), and from the diagram, \( AC=8\space\text{cm}\).

Step3: Calculate \(\tan A\)

Using the formula for tangent, we substitute the lengths of the opposite and adjacent sides:
\(\tan A=\frac{BC}{AC}=\frac{6}{8}=\frac{3}{4}\) (or we can write it as \( \frac{6}{8}\) or \( \frac{3}{4}\))

Answer:

\( 6/8 \) or \( 3/4 \) (the option corresponding to this value)