Question

A straight line inserted at the origin terminates at the point (6, 7) as it sweeps out an angle θ in standard position. Which of the following corresponds to the evaluation of tanθ ;

Answer 1

Answer:

The value of $\tan \theta$ is $\frac{7}{6}$.

Step-by-step explanation:

It is given that a straight line inserted at the origin terminates at the point (6, 7) as it sweeps out an angle θ in standard position.

Draw a diagram using the given information.

From the given graph it is clear that it is a right angled triangle with base 6 and height 7.

According to the trigonometric ratios,

$\tan \theta=\frac{perpendicular}{base}$

Substitute perpendicular=7 and base=6 in the above equation.

$\tan \theta=\frac{7}{6}$

Therefore the value of $\tan \theta$ is $\frac{7}{6}$.

Answer 2

Since the line stops at the point (6, 7), then it means that the height of the triangle made is 7 units and the base is 6 units long.
An angle, θ, is made at the line that joins the origin and the point (6, 7).

$tan \theta = \frac{opp}{adj}$
$tan \theta = \frac{height}{base} = \frac{7}{6}$

Hence, $tan \theta = \frac{7}{6}$