Question

ab =
round your answer to the nearest hundredth.
right triangle with right angle at c, ac = 4, angle at a is 25 degrees, ab is the hypotenuse (marked with ?)
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Explanation:

Step1: Identify trigonometric ratio

In right triangle \( \triangle ABC \), \( \angle C = 90^\circ \), \( AC = 4 \), \( \angle A = 25^\circ \). We use cosine: \( \cos(\angle A)=\frac{AC}{AB} \).

Step2: Solve for \( AB \)

Rearrange: \( AB = \frac{AC}{\cos(\angle A)} \). Substitute \( AC = 4 \), \( \angle A = 25^\circ \): \( AB=\frac{4}{\cos(25^\circ)} \). Calculate \( \cos(25^\circ)\approx0.9063 \), so \( AB\approx\frac{4}{0.9063}\approx4.41 \).

Answer:

\( 4.41 \)