Question

3. An acute angle θ is in a right triangle with cos θ = two thirds . What is the value of sec θ? (2 points) five divided by two two divided by square root of five square root of five divided by three three halves

Answer 1

Answer: sec θ =
`(3)/(2)`

Explanation:

cos θ =
`(adjacent)/(hypotenuse)` =
`(2)/(3)`

sec θ =
`(hypotenuse)/(adjacent)` =
`(3)/(2)`

Extra Credit: Use Pythagorean Theorem to find the opposite side

2² + b² = 3²

4 + b² = 9

b² = 5

b = √5

sin θ =
`(opposite)/(hypotenuse)` =
`(√(5))/(3)`

csc θ =
`(hypotenuse)/(opposite)` =
`(3)/(√(5))` =
`(3√(5))/(5)}`