Question

determine the value of x to the nearest cm.

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

Explanation:

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

In \( \triangle DEF \), \( \sin35^{\circ}=\frac{DF}{DE} \), but we can also use \( \tan35^{\circ}=\frac{DF}{EF} \). Given \( EF = 99\mathrm{cm} \), so \( DF=EF\times\tan35^{\circ}=99\times\tan35^{\circ}\approx99\times0.7002 = 69.3198\mathrm{cm} \)

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

In \( \triangle DFG \), \( \sin45^{\circ}=\frac{DF}{x} \). Since \( \sin45^{\circ}=\frac{\sqrt{2}}{2}\approx0.7071 \) and \( DF\approx69.3198\mathrm{cm} \), then \( x=\frac{DF}{\sin45^{\circ}}=\frac{69.3198}{0.7071}\approx98\mathrm{cm} \)

Answer:

A. 98 cm