Respuesta :
Answer: the required value is [tex]\sec \theta=\dfrac{3}{2}.[/tex]
Step-by-step explanation: Given that an acute angle θ is in a right triangle with cos θ = two thirds.
We are to find the value of sec θ.
In a right-angled triangle, we have the following relation between the cos and sec of an acute angle θ :
[tex]\sec \theta=\dfrac{1}{\cos \theta}.[/tex]
From the given information, we have
[tex]\cos \theta=\dfrac{2}{3}.[/tex]
Therefore, we get
[tex]\sec \theta=\dfrac{1}{\cos \theta}=\dfrac{1}{\frac{2}{3}}=1\times\dfrac{3}{2}=\dfrac{3}{2}.[/tex]
Thus, the required value is
[tex]\sec \theta=\dfrac{3}{2}.[/tex]
