Question

find one solution for the equation. assume that all angles involved are acute angles. sin(2θ - 25°) = cos(3θ - 10°) θ = □° (simplify your answer.)

Explanation:

Step1: Use co - function identity

We know that $\sin A=\cos(90^{\circ}-A)$. So, if $\sin(2\theta - 25^{\circ})=\cos(3\theta - 10^{\circ})$, then $2\theta-25^{\circ}+3\theta - 10^{\circ}=90^{\circ}$.

Step2: Combine like - terms

Combining the $\theta$ terms and the constant terms on the left - hand side gives $(2\theta+3\theta)+(-25^{\circ}-10^{\circ}) = 90^{\circ}$, which simplifies to $5\theta-35^{\circ}=90^{\circ}$.

Step3: Isolate the variable $\theta$

Add $35^{\circ}$ to both sides of the equation: $5\theta=90^{\circ}+35^{\circ}$, so $5\theta = 125^{\circ}$. Then divide both sides by 5: $\theta=\frac{125^{\circ}}{5}$.

Answer:

$25$