Question

find the tangent of $\angle b$. simplify your answer and write it as a proper fraction, improper fraction, or whole number. $\tan (b) = \square$

Explanation:

Step1: Recall tangent definition

For right triangle, $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$

Step2: Find side length BC

Use Pythagorean theorem: $BC=\sqrt{AB^2-AC^2}$
$BC=\sqrt{68^2-60^2}=\sqrt{4624-3600}=\sqrt{1024}=32$

Step3: Identify sides for ∠B

Opposite side to ∠B is $AC=60$, adjacent side is $BC=32$

Step4: Calculate tan(B)

$\tan(B)=\frac{60}{32}=\frac{15}{8}$

Answer:

$\frac{15}{8}$