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

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 = (opp)/(adj)`

`tan \theta = (height)/(base) = (7)/(6)`

Hence,
`tan \theta = (7)/(6)`

Answer 2

The value of
`\tan \theta` is
`(7)/(6)`.

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=(perpendicular)/(base)`

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

`\tan \theta=(7)/(6)`

Therefore the value of
`\tan \theta` is
`(7)/(6)`.