Question

Can someone explain this to me?

Answer 1

Explanation:

a). By applying tangent rule in the triangle,

tanθ =
`\frac{\text{Opposite side}}{\text{Adjacent side}}=(3)/(4)`

θ =
`\text{tan}^(-1)((3)/(4))`

θ = 36.87°

Therefore, θ < 45°

b). By using cosine rule in this triangle,

cosθ =
`\frac{\text{Adjacent side}}{\text{Hypotenuse}}=(18)/(18√(2))`

cosθ =
`(1)/(√(2))`

θ = 45°

c). By using tangent rule,

tanθ =
`\frac{\text{Opposite side}}{\text{Adjacent side}}=(8)/(2)`

θ =
`\text{tan}^(-1)(4)`

θ = 75.96°

θ > 45°