Question

ac =
round your answer to the nearest hundredth.
(image of a right triangle with right angle at c, bc = 3, angle at a is 35 degrees, ac is the unknown side we need to find)

Explanation:

Step1: Identify trigonometric ratio

We use tangent: $\tan(A) = \frac{BC}{AC}$

Step2: Rearrange to solve for AC

$AC = \frac{BC}{\tan(A)}$

Step3: Substitute known values

$BC=3$, $A=35^\circ$, so $AC = \frac{3}{\tan(35^\circ)}$

Step4: Calculate and round

$\tan(35^\circ) \approx 0.7002$, so $AC \approx \frac{3}{0.7002} \approx 4.28$

Answer:

4.28