Answer:
sin θ = (√21) / 5
tan θ = (√21) / 2
Step-by-step explanation:
Remember the formulas for the <u>trigonometry ratios</u> 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 <u>Pythagorean Theorem</u>. 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. <u>Use the trigonometry ratios</u> to find sine and tangent.
sin θ = opposite / hypotenuse
sin θ = (√21) / 5
tan θ = opposite / adjacent
tan θ = (√21) / 2
