Question

Solve for DB
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Answer 1

$\\ \sf\longmapsto CD^2=AD\times DB$

$\\ \sf\longmapsto 12^2=16DB$

$\\ \sf\longmapsto 144=16DB$

$\\ \sf\longmapsto DB=\dfrac{144}{16}$

$\\ \sf\longmapsto DB=8$

Answer 2

Answer:

• let's first consinder triangle ADC

• from trigonometric ratios:

$\hookrightarrow \: { \rm{ \tan( \theta) = \frac{opposite}{adjacent} }}$

→ theta is the angle CAD

→ opposite is 16

→ adjacent is 12

${ \tt{ \tan( \theta) = \frac{16}{12} }} \\ \\ { \tt{ \theta = { \tan }^{ - 1}( \frac{16}{12} ) }} \\ \\ { \underline{ \tt{ \: \: \theta = 53.1 \degree \: }}}$

Then let's find the angle BCD

${ \tt{ \angle BCD + \angle CAD = 90 \degree}} \\ { \tt{\angle BCD + 53.1 \degree = 90 \degree}} \\ { \underline{ \tt{ \: \: \angle BCD = 36.9 \degree \: \: }}}$

• from trigonometric ratios:

${ \rm{ \tan( \theta) = \frac{opposite}{adjacent} }}$

→ theta is 36.9°

→ opposite is DB

→ adjacent is 12

${ \tt{ \tan(36.9) = \frac{DB}{12} }} \\ \\ { \tt{DB = 12 \times \tan(36.9) }} \\ \\ { \tt{DB = 12 \times 0.75}} \\ \\ { \rm{answer : \: { \boxed{ \rm{ \: \: DB = 9 \: \: }}}}}$