Question

An electric pole, 14 metres high, casts a shadow of 10 metres. Find the height of a tree that casts a shadow of 15m under the similar conditions

Answer 1

Step-by-step explanation:

Question:-

An electric pole, 14 metres high, casts a shadow of 10 metres. Find the height of a tree that casts a shadow of 15m under the similar conditions

Solution:-

Let's understand the concept:-

here a electric pole and the shadow and the distance between the peaks of both creates a right angled triangle so the tree and shadow creates the same .

Here,

• in electric poll and shadow

perpendicular =p=14m

base=b=10m

hypontenuse =h

According to Pythagorean theory

${:}\longrightarrow$${\boxed{{p}^{2}+{b}^{2}={h}^{2}}}$

${:}\longrightarrow$$h={\sqrt{{p}^{2}+{b}^{2}}}$

${:}\longrightarrow$${\sqrt {{14}^{2}+{10}^{2}}}$

${:}\longrightarrow$${\sqrt {196+100}}$

${:}\longrightarrow$${\sqrt{296}}$

${:}\longrightarrow$${\underline{\boxed {h={\sqrt {296}}m}}}$

Now,

In tree and shadow pole case

base=b=15m

hypontenuse =h=17 ${\sqrt {3}}$

perpendicular=p

again using Pythagorean theory

${:}\longrightarrow$$p={\sqrt {{h}^{2}-{b}^{2}}}$

${:}\longrightarrow$${\sqrt {({{\sqrt {296}})}^{2}-{15}^{2}}}$

${:}\longrightarrow$${\sqrt {296-225}}$

${:}\longrightarrow$${\sqrt{71}}$

${:}\longrightarrow$$8 {\sqrt {3}}m$

${:}\longrightarrow$approximately 8m

${:}\longrightarrow$${\underline{\boxed{\bf {h=8m}}}}$

• Hence

height of the tree =8m