Question

question 2 (mandatory) (1 point)
determine the value of x to the nearest cm.

a) 68 cm
b) 47 cm
c) 98 cm
d) 74 cm

Explanation:

Step1: Find \(DF\) using \(\triangle DEF\)

In right - triangle \(DEF\), \(\sin35^{\circ}=\frac{DF}{DE}\), and \(DE = 99\) cm. So \(DF = 99\times\sin35^{\circ}\approx99\times0.5736\approx56.8\) cm.

Step2: Find \(x\) using \(\triangle DFG\)

In right - triangle \(DFG\), \(\sin45^{\circ}=\frac{DF}{x}\). Since \(DF\approx56.8\) cm and \(\sin45^{\circ}=\frac{\sqrt{2}}{2}\approx0.707\), then \(x=\frac{DF}{\sin45^{\circ}}\approx\frac{56.8}{0.707}\approx74\) cm.

Answer:

d) \(74\) cm