Question

find one solution for the equation. assume that all angles involved are acute angles. tan (3b - 52°)= cot (5b - 10°)
b = □°
(simplify your answer.)

Explanation:

Step1: Use co - function identity

We know that $\tan\theta=\cot(90^{\circ}-\theta)$. So, $\tan(3B - 52^{\circ})=\cot(90^{\circ}-(3B - 52^{\circ}))$.
Since $\tan(3B - 52^{\circ})=\cot(5B - 10^{\circ})$, then $\cot(90^{\circ}-(3B - 52^{\circ}))=\cot(5B - 10^{\circ})$.
This gives $90-(3B - 52)=5B - 10$.

Step2: Simplify the equation

First, expand the left - hand side: $90-3B + 52=5B - 10$.
Combine like terms: $142-3B=5B - 10$.
Add $3B$ to both sides: $142=5B - 10+3B$.
So, $142 = 8B-10$.
Add 10 to both sides: $142 + 10=8B$, i.e., $152 = 8B$.

Step3: Solve for B

Divide both sides by 8: $B=\frac{152}{8}=19$.

Answer:

$19$