Question

Please helpppp (::: this is hard

Answer 1

Answer:

sin θ = (√21) / 5

tan θ = (√21) / 2

Step-by-step explanation:

Remember the formulas for the trigonometry ratios with SohCahToa:

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

If cos θ = 2/5, then:

adjacent = 2

hypotenuse = 5

Remember all right triangles follow the Pythagorean Theorem. So if you are missing one side, you can solve.

Let's find the opposite side.

a² + b² = c²

2² + b² = 5²

4 + b² = 25

b² = 21

b = √21

opposite = √21

Now we know all three sides. Use the trigonometry ratios to find sine and tangent.

sin θ = opposite / hypotenuse

sin θ = (√21) / 5

tan θ = opposite / adjacent

tan θ = (√21) / 2