Question

Plz answer question in screen shot

Answer 1

Answer:

tan theta = 2 sqrt(5) /15

Step-by-step explanation:

sin theta = opp / hypotenuse

sin theta = 2/7

We can use the Pythagorean theorem to find the length of the adjacent side

a^2 + b^2 = c^2

2^2 +adj^2 = 7^2

4 + adj^2 = 49

adj ^2 = 49-4

adj^2 = 45

Taking the square root of each side

adj = sqrt(45) = sqrt(9*5) =sqrt(9) sqrt(5) = 3 sqrt(5)

The tan theta = opp/ adj

tan theta = 2 / 3 sqrt(5)

Multiply by sqrt(5) / sqrt(5)

                = 2 sqrt(5) / 3 *5

                 = 2 sqrt(5) /15