Question

A pole of 8m cast a shadow of 10m find the hight of tree cast a shadow of 40m

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Height\:of\:tree=32\:m}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given:}} \\ \tt: \implies Height\: of \: pole = 8 \: m \\ \\ \tt: \implies Shadow \: of \: pole = 10 \: m \\ \\ \tt: \implies Shadow \: of \: tree = 40 \: m \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Height \: of \: tree = ?$

• According to given question :

$\circ \: \tt{Let \: angle \: of \: elevation \: for \: both \: pole \: and \: tree \: be \: \alpha } \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies tan \: \alpha = \frac{Perpendicular}{Base} \\ \\ \tt: \implies tan \: \alpha = \frac{8}{10} \\ \\ \tt: \implies tan \: \alpha = 0.8 \\ \\ \bold{For \: tree : } \\ \tt: \implies tan \: \alpha = \frac{Perpendicular}{Base} \\ \\ \tt: \implies 0.8 = \frac{h}{40} \\ \\ \tt: \implies 0.8 \times 40 = h \\ \\ \green{\tt: \implies h = 32 \: m} \\ \\ \green{\tt \therefore Height \: of \: tree \: is \: 32 \: m}$

Answer 2

Answer:

The height of the tree is 32m

Step-by-step explanation:

Let us consider

• the pole be CD

• the tree be AB

• Shadow of pole DO

• Shadow of tree BO

• Let the angle AOB = ø

We are given ,

CD = 8m

DO = 10m

and BO = 40m

From the trigonometric functions we have

$\tan\theta = \frac{</u></strong><strong><u>P</u></strong><strong><u>erpendicular}{</u></strong><strong><u>B</u></strong><strong><u>ase}$

So here

$\tan \theta = \frac{</u></strong><strong><u>CD</u></strong><strong><u>}{</u></strong><strong><u>DO</u></strong><strong><u> } \\ \implies \tan \theta = \frac{8m}{10m} \\ \implies \tan \theta = \frac{8}{10}$

Now we have from triangle AOB

$\tan \theta = \frac{AB}{BO} \\ \implies \frac{8}{10} = \frac{AB}{40} \\ \implies AB = \frac{8 \times 40}{10} \\ \implies AB = 32$

Therefore , height of the tree , AB = 32m