Question

. Find the value of sec θ for the angle shown. (2 points) A line is drawn from the origin through the point seven comma six. The angle theta is given as the measurement from the positive x axis counterclockwise to the line. sec θ = seven times square root of eighty-five divided by eighty-five sec θ = six-sevenths sec θ = seven sixths sec θ = square root of eighty-five divided by eighty-five

Answer 1

The value of sec θ is:

`\sec \theta=(√(85))/(7)`

Explanation:

We know that the the trignometric ratio secant theta is the ratio of the hypotenuse to the adjacent side of the triangle corresponding to the angle theta.

We can model this situation with the help of a right triangle Δ ABC

such that the hypotenuse is side AC.

Now using the Pythagorean Theorem in the triangle Δ ABC we get:

`AC^2=AB^2+CB^2\\\\i.e.\\\\AC^2=6^2+7^2\\\\i.e.\\\\AC^2=85\\\\i.e.\\\\AC=√(85)`

Hence, the secant ratio corresponding to theta is given by:

`\sec \theta=(AC)/(CB)\\\\i.e.\\\\\sec \theta=(√(85))/(7)`

Answer 2

Answer:
`(√(85))/(7)`

Explanation:

(7, 6)

Use Pythagorean Theorem to find the hypotenuse:

7² + 6² = c²

49 + 36 = c²

85 = c²

√85 = c

adjacent = 7, opposite = 6, hypotenuse = √85

sec θ =
`(hypotenuse)/(adjacent)` =
`(√(85))/(7)`