If angle B measures 25^circ what is the approximate perimeter of the triangle below? 10.3 units 11.8 units 22.1 units 25.2 units

To find the perimeter of the right triangle ABC, we need to find the lengths of all three sides: AB, BC, and AC. We already know that AB = 4 units and that ∠A is a right angle, which means that ∠C is \(90^{\circ} - 25^{\circ} = 65^{\circ}\).Step 1: Find the length of AC (the adjacent side to ∠B) using the cosine function.\[\cos(B) = \frac{adjacent}{hypotenuse}\]\[\cos(25^{\circ}) = \frac{AB}{AC}\]\[AC = \frac{AB}{\cos(25^{\circ})}\]\[AC = \frac{4}{\cos(25^{\circ})}\]Using a calculator, we find that:\[\cos(25^{\circ}) \approx 0.9063\]\[AC \approx \frac{4}{0.9063}\]\[AC \approx 4.4142 \text{ units}\]Step 2: Find the length of BC (the opposite side to ∠B) using the sine function.\[\sin(B) = \frac{opposite}{hypotenuse}\]\[\sin(25^{\circ}) = \frac{BC}{AC}\]\[BC = AC \cdot \sin(25^{\circ})\]\[BC = 4.4142 \cdot \sin(25^{\circ})\]Using a calculator, we find that:\[\sin(25^{\circ}) \approx 0.4226\]\[BC \approx 4.4142 \cdot 0.4226\]\[BC \approx 1.8651 \text{ units}\]Step 3: Calculate the perimeter by adding the lengths of all three sides.\[\text{Perimeter} = AB + AC + BC\]\[\text{Perimeter} \approx 4 + 4.4142 + 1.8651\]\[\text{Perimeter} \approx 10.2793 \text{ units}\]The closest answer to our calculation is 10.3 units, so the approximate perimeter of the triangle is:Answer: 10.3 units