Question

a flag post stands on a building.from a point on the ground the angle of elevation of the top and bottom of the flag post is 60 and 45 degree respectively.if the h of the flag post is 10m,find the h of the building.

Answer 1

Answer:

6

Step-by-step explanation:

Answer 2

The height of building=BC=$5(\sqrt 3+1)$ m

Step-by-step explanation:

Height of flag post=h=10 m

In triangle BCD

$tan\theta=\frac{perpendicular\;side}{Base}$

$\theta=45^{\circ}$

Substitute the values then we get

$tan45=\frac{BC}{CD}$

$\frac{BC}{CD}=1$

Because tan 45 degrees=1

$BC=CD$

In triangle ABD

$\frac{AC}{CD}=tan60$

$\frac{10+BC}{CD}=\sqrt 3$

Because $tan60=\sqrt 3$

$\frac{10+BC}{BC}=\sqrt 3$

$10+BC=BC\sqrt 3$

$10=BC\sqrt 3-BC$

Let BC=x

$10=x\sqrt 3-x=x(\sqrt 3-1)$

$x=\frac{10}{\sqrt 3-1}\times \frac{\sqrt 3+1}{\sqrt 3+1}$

$x=\frac{10(\sqrt 3+1)}{(\sqrt 3)^2-1}=\frac{10(\sqrt 3+1)}{3-1}$

By using property:$(a+b)(a-b)=a^2-b^2$

$x=\frac{10(\sqrt 3+1)}{2}=5(\sqrt 3+1)$

Hence, the height of building=BC=$5(\sqrt 3+1)$ m

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