Answer: [tex]\frac{\sqrt{85}}{7}[/tex]
Step-by-step 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 = [tex]\frac{hypotenuse}{adjacent}[/tex] = [tex]\frac{\sqrt{85}}{7}[/tex]
The value of sec θ is:
[tex]\sec \theta=\dfrac{\sqrt{85}}{7}[/tex]
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:
[tex]AC^2=AB^2+CB^2\\\\i.e.\\\\AC^2=6^2+7^2\\\\i.e.\\\\AC^2=85\\\\i.e.\\\\AC=\sqrt{85}[/tex]
Hence, the secant ratio corresponding to theta is given by:
[tex]\sec \theta=\dfrac{AC}{CB}\\\\i.e.\\\\\sec \theta=\dfrac{\sqrt{85}}{7}[/tex]
