In a right triangle, sin θ = 9/15. Find the value of tan θ
it is evidently a 9-12-15 triangle, so
tanθ = 9/12
To find the value of tan θ given sin θ, we can use the formula for tangent:
tan θ = sin θ / cos θ
To find cos θ, we can use the Pythagorean identity for right triangles:
sin² θ + cos² θ = 1
Since we already know the value of sin θ, we can substitute it in the equation and solve for cos θ.
(9/15)² + cos² θ = 1
81/225 + cos² θ = 1
cos² θ = 1 - 81/225
cos² θ = 144/225
cos θ = √(144/225)
cos θ = 12/15
cos θ = 4/5
Now that we have both sin θ and cos θ, we can substitute them into the formula for tangent:
tan θ = sin θ / cos θ
tan θ = (9/15) / (4/5)
tan θ = (9/15) * (5/4)
tan θ = (9 * 5) / (15 * 4)
tan θ = 45/60
tan θ = 3/4
Therefore, the value of tan θ is 3/4.