Question

An acute angle θ is in a right triangle with cos θ = two thirds. What is the value of sec θ?

Answer 1

cos θ = 2/3
hence sec θ = 1 / cos θ
sec θ = 3/2

Answer 2

Answer: the required value is
`\sec \theta=(3)/(2).`

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 :

`\sec \theta=(1)/(\cos \theta).`

From the given information, we have

`\cos \theta=(2)/(3).`

Therefore, we get

`\sec \theta=(1)/(\cos \theta)=(1)/((2)/(3))=1*(3)/(2)=(3)/(2).`

Thus, the required value is

`\sec \theta=(3)/(2).`