Question

right triangle relationships and trigonometry. the equation tan(55°) = 15/h can be used to find the length of ac. what is the length of ac? round to the nearest tenth. 12.8 cm. 10.5 cm. 9.8 cm.

Explanation:

Step1: Recall tangent formula

In right - triangle \(ABC\) with right - angle at \(C\), \(\tan(A)=\frac{BC}{AC}\). Given \(A = 55^{\circ}\) and \(BC = 15\) cm, and let \(AC = h\). So \(\tan(55^{\circ})=\frac{15}{h}\).

Step2: Solve for \(h\)

We know that \(\tan(55^{\circ})\approx1.4281\). Then \(h=\frac{15}{\tan(55^{\circ})}\). Substituting the value of \(\tan(55^{\circ})\), we get \(h=\frac{15}{1.4281}\approx10.5\) cm.

Answer:

10.5 cm