Question

From the figure, given below, calculate the length of CD.

Answer 1

In right ΔACB, we have

${\displaystyle \tan \theta =\frac{AB}{BC}}$

${\displaystyle \Rightarrow {\tan 47}^{\circ }=\frac{AB}{15}}$

${\displaystyle \Rightarrow 1.0724=\frac{AB}{15}}$

∴ AB = 1.0724 × 15

= 16.0860 m

= 16.09 m.

And in right ΔADE, we have

${\displaystyle {\tan 22}^{\circ }=\frac{AE}{DE}}$

${\displaystyle \Rightarrow 0.4040=\frac{AE}{15}}$

∴ AE = 15 × 0.4040

= 6.0600

= 6.06 m.

∴ CD = EB

= AB – AE

= 16.09 – 6.06

= 10.03 m