Question

ab =
round your answer to the nearest hundredth.
triangle with points a, b, c (right angle at c), bc = 3, angle at b is 65°, ab (hypotenuse) marked with ?

Explanation:

Step1: Identify the trigonometric relationship

In right triangle \(ABC\) (right - angled at \(C\)), we know that \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 65^{\circ}\), the adjacent side to \(\theta\) is \(BC = 3\), and the hypotenuse is \(AB\) (which we need to find). So, \(\cos(65^{\circ})=\frac{BC}{AB}\), which can be rewritten as \(AB=\frac{BC}{\cos(65^{\circ})}\).

Step2: Substitute the values and calculate

We know that \(BC = 3\) and \(\cos(65^{\circ})\approx0.4226\). Substituting these values into the formula \(AB=\frac{3}{\cos(65^{\circ})}\), we get \(AB=\frac{3}{0.4226}\approx7.10\) (rounded to the nearest hundredth).

Answer:

\(7.10\)