Question

ab =
round your answer to the nearest hundredth.
c 4 a
25°
b

Explanation:

Step1: Identify the cosine - ratio in right - triangle

In right - triangle $ABC$ with right - angle at $C$, $\cos(A)=\frac{AC}{AB}$. We know that $AC = 4$ and $A=25^{\circ}$.

Step2: Rearrange the formula to solve for $AB$

From $\cos(A)=\frac{AC}{AB}$, we can rewrite it as $AB=\frac{AC}{\cos(A)}$.

Step3: Substitute the known values

Substitute $AC = 4$ and $A = 25^{\circ}$ into the formula. $\cos(25^{\circ})\approx0.9063$. Then $AB=\frac{4}{\cos(25^{\circ})}$.

Step4: Calculate the value of $AB$

$AB=\frac{4}{0.9063}\approx4.41$.

Answer:

$4.41$