Question

l will MARK BRAINLIST


if the angle of elevation of the top of two Statues Of height M1 and M2 are 60° and 30° respectively from the midpoint of the line segment joining their feet then find the ratio M1:M2

Answer 1

Answer:

AB=m1  and CD=m2

angle AOB is 60 and other is 30

BO=OD=x as it is the mid point

tan 60=root3=m1/x

m1=root3(x)

tan 30=1/root3=m2/x

m2=x/root3

m1:m2=root3(x)*root3/x

3/1=3:1

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Answer 2

We need to recall the following trigonometric ratios.

• $tan30\textdegree=\frac{1}{\sqrt{3} }$
• $tan60\textdegree=\sqrt{3}$

Given:

the angle of elevation of the top of two Statues from the midpoint of the line segment joining,

For statue of height $M_1$ is $60\textdegree$

For statue of height $M_2$ is $30\textdegree$

Let $2m$ be the distance between the statues.

From $\triangle ABC$ , we get

$tan60\textdegree=\frac{AB}{BC}$

$\sqrt{3} =\frac{M1}{m}$

$m=\frac{M1}{\sqrt{3} }$               ........$(1)$

From $\triangle CDE$, we get

$tan30\textdegree=\frac{DE}{CD}$

$\frac{1}{\sqrt{3} } =\frac{M_2}{m}$

$m=\sqrt{3} M_2$         ........$(2)$

From equations $(1)$ and, $(2)$, we get

$\frac{M_1}{\sqrt{3} } =\sqrt{3}M_2$

$\frac{M_1}{M_2} =\sqrt{3} \cdot \sqrt{3}$

$\frac{M_1}{M_2} =3$

Hence, the ratio is $\frac{M_1}{M_2}=\frac{3}{1}$