Question

△abc ~ △def
note: images are not drawn to scale.
what is cos b?
cos b = \square

Explanation:

Step1: Identify side lengths for ∠B

In right △ABC, for ∠B: adjacent side $AB=90$, opposite side $AC=120$. First find hypotenuse $BC$.
$$BC = \sqrt{AB^2 + AC^2} = \sqrt{90^2 + 120^2}$$

Step2: Calculate hypotenuse length

Compute the value of the hypotenuse.
$$BC = \sqrt{8100 + 14400} = \sqrt{22500} = 150$$

Step3: Apply cosine definition

Cosine of an angle is adjacent over hypotenuse.
$$\cos B = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{AB}{BC} = \frac{90}{150}$$

Step4: Simplify the fraction

Reduce the fraction to lowest terms.
$$\cos B = \frac{3}{5}$$

Answer:

$\frac{3}{5}$