Question

if angle b measures 25°, what is the approximate perimeter of the triangle? 11.8 units 22.1 units 10.3 units 28.2 units

Explanation:

Step1: Find side AC using tangent

In right - triangle ABC, $\tan B=\frac{AC}{AB}$. Given $B = 25^{\circ}$ and $AB = 4$. So $AC=AB\times\tan B=4\times\tan(25^{\circ})$. Since $\tan(25^{\circ})\approx0.4663$, then $AC\approx4\times0.4663 = 1.8652$.

Step2: Find side BC using cosine

$\cos B=\frac{AB}{BC}$, so $BC=\frac{AB}{\cos B}$. Since $\cos(25^{\circ})\approx0.9063$, then $BC=\frac{4}{\cos(25^{\circ})}\approx\frac{4}{0.9063}\approx4.4135$.

Step3: Calculate the perimeter

The perimeter $P$ of $\triangle ABC$ is $P = AB + AC+BC$. Substitute $AB = 4$, $AC\approx1.8652$, and $BC\approx4.4135$ into the formula. $P\approx4 + 1.8652+4.4135=10.2787\approx10.3$ units.

Answer:

10.3 units