Question

you might need: calculator
bc =
round your answer to the nearest hundredth.
(there is a right triangle abc with right angle at c, angle at b is 50 degrees, length of ac is 7, and we need to find the length of bc)

Explanation:

Step1: Identify trigonometric ratio

In right triangle \(ABC\) (right-angled at \(C\)), we know angle \(B = 50^\circ\) and side \(AC = 7\). We need to find \(BC\). The tangent of angle \(B\) is \(\tan(B)=\frac{AC}{BC}\).
So, \(\tan(50^\circ)=\frac{7}{BC}\)

Step2: Solve for \(BC\)

Rearrange the formula: \(BC = \frac{7}{\tan(50^\circ)}\)
Using a calculator, \(\tan(50^\circ)\approx1.191753592\)
Then \(BC=\frac{7}{1.191753592}\approx5.87\)

Answer:

\(5.87\)