Answer :

The value of theta to the nearest degree is 66°.

Using the given values of the opposite and adjacent sides of the right-angled triangle, we can use the trigonometric relation:

tan θ = opposite / adjacent

Substituting the given values, we get:

tanθ= 16/7

To find the value of theta, we can take the inverse tangent (or arctan) of both sides:

θ=tan ⁻¹ (16/7)

Using a calculator, we get:

θ ≈ 66.37°

Therefore, the value of theta to the nearest degree is 66°.