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 ;

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).

[tex]tan \theta = \frac{opp}{adj}[/tex]
[tex]tan \theta = \frac{height}{base} = \frac{7}{6}[/tex]

Hence, [tex]tan \theta = \frac{7}{6}[/tex]

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erinna erinna · Answer 2 · 2019-07-03T12:56:52+02:00

Answer:

The value of [tex]\tan \theta[/tex] is [tex]\frac{7}{6}[/tex].

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,

[tex]\tan \theta=\frac{perpendicular}{base}[/tex]

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

[tex]\tan \theta=\frac{7}{6}[/tex]

Therefore the value of [tex]\tan \theta[/tex] is [tex]\frac{7}{6}[/tex].