The arc length of a sector is 88m and radius is 42m. Find the \$\theta\$ ?

Arc length of a sector.

l = \$\frac{\theta}{360^\circ} \times 2 \times \pi r\$

Substitute \$22/7\$ for \$pi\$, 42 for r and 88 for l.

88 = \$\frac{\theta}{360°} \times 2 \times \frac{22}{7} \times 42\$

Cancel out common factor.

\$\cancel{88}^8 = \frac{\theta}{360°} \times 2 \times \frac{\cancel{22}^2}{7} \times 42 \$

Cancel out common factor.

\$8 = \frac{\theta}{360°} \times 2 \times \frac{2}{\cancel{7}^1} \times \cancel{42}^6 \$

Cancel out common factor.

\$\cancel{8}^4 = \frac{\theta}{360°} \times 2 \times \frac{\cancel{2}^1}{1} \times 6 \$

Cancel out common factor.

\$\cancel{4}^2 = \frac{\theta}{360°} \times \cancel{2}^1 \times \frac{1}{1} \times 6 \$

Cancel out common factor.

\$2&= \frac{\theta}{\cancel{360°} ^{60°}} \times 1 \times \frac{1}{1} \times \cancel{6}^1 \$

Multiply.

\$2 = \frac{\theta}{60°} \$

Solve for \$\theta\$.

\$\theta = 120° \$

Answer

The θ is \$120°\$.