Question

a person of 6 feet height observes the top of a building from a point at a distance of 30 feet from the base of the building if the angle of elevation is 45 degree find the height of the building

Answer 1

$\huge\underline\mathfrak{Subject:-}$

Math

$\huge\underline\mathfrak{Topic:-}$

Application of Trigonometry

$\textbf{Some Important point }$

$\textbf{Defination Related to topic}$

$\textbf{(1)Angle of Elevations}$

The angle of elevation of a point is the angle formed between line of sight and horizontal line .

$\huge\underline\mathfrak{Figure}$

Look in attachment

$\huge\underline\mathfrak{Solution}$

$\textbf{Step (1)}$

$\huge\underline\mathfrak{construction}$

look in attachment also

Let AB be the height of building = x feet or (AE+EB)

Height of person(Dc) = 6 feet

Distance of person from building (CB)= 30 feet

Angle of elevation = 45°

So, look in attachment in fig

join D and E

so ,Now $\textbf{DECB}$. DE is equal to CB opposite side of Rectangle are equal.

=> DE= 30 feet and EB = 6 feet

$\textbf{ Determine ,AE}$

using, $\textbf{Trigonometry ratio}$

In a right ∆ AED

$\angle {ADE}$=45°

DE=30feet

1=\frac{AE}{DE}

i.e, 1 = \frac{AE}{30}

AE=30 feet

$\therefore$. AE= 30 feet

so the height of building (AB)= ( AE+EB) feet

= (30+6)feet

= 36 feet



$\huge\underline\mathfrak{Hence}$

Height of building ( AE)=36 feet