Question

Use the following triangle to find Sec theta.

Note: enter the exact, fully simplified and rationalized answer

Answer 1

`(√(41))/(4)`

Explanation:

sec(theta) is defined as:
`sec(\theta)=(1)/(cos(\theta)) = (hypotenuse)/(adjacent)`

In the diagram you provided the hypotenuse of the triangle is sqrt(41) and the opposite side is 5, using these two sides, we can solve for the adjacent side by using the Pythagorean Theorem:
`a^2+b^2=c^2`

So this gives us the equation where a=adjacent side:

`a^2+5^2=√(41)^2`

`a^2+25=41`

Subtract 25 from both sides

`a^2=16`

Take the square root of both sides

`a=4`

So now plug this into the definition of sec(theta) and you get:
`(√(41))/(4)`. This is in most simplified form since 41, has no factors besides 41 and 1.