Question

(i) From the roof of a house of 11 meter high, the angles of question of de topand foot of a lamp post are 30° and 60° respectively. Find the heght of the lamp post.​

Answer 1

★Given →

• The height of the house (AC)= 11 m
• The angles of depression of the top and foot of the lamp post are 30° and 60°.

angle FAE = 30° , angle FAD=60°

★To find →

The height of the lamp post.

★Solution→

In the attachment, AC is the height of the house and ED is the height of the lamp post.

•angle FAE = angle AEB = 30°

•angle FAD = angle ACD = 60°

∆ACD is a right triangle.

$\frac{ac}{cd} = \tan(60) \\ = > \frac{11}{cd} = \sqrt{3} \\ = > cd \sqrt{3} = 11 \\ = > cd = \frac{11}{ \sqrt{3} }$

CD||BE and CD = BE

$cd = be = \frac{11}{ \sqrt{3} } m$

Again,

∆ ABE is a right triangle.

$\frac{ab}{be} = \tan(30) \\ = > \frac{ab}{ \frac{11}{ \sqrt{3} } } = \frac{1}{ \sqrt{3} } \\ = > \frac{ab \sqrt{3} }{11} = \frac{1}{ \sqrt{3} } \\ = > 3ab = 11 \\ = > ab = \frac{11}{3}$

$ab = \frac{11}{3} \: m$

•To find the value of BC ,we need to substrate AB from AC.

AC = 11 m

BC = AC- AB

$= 11 - \frac{11}{3 } \\ = \frac{22}{3} \\ = 7.33(approx)$

So, the height of the lamp post is 7.33 (approx) m.

★Answer→

The height of the lamp post is 7.33 (approx) meter.

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Answer 2

Answer:

★Answer→

The height of the lamp post is 7.33 (approx) meter

★Given →

The height of the house (AC)= 11 m

The angles of depression of the top and foot of the lamp post are 30° and 60°.

angle FAE = 30° , angle FAD=60°

★To find →

The height of the lamp post.

★Solution→

In the attachment, AC is the height of the house and ED is the height of the lamp post.

•angle FAE = angle AEB = 30°

•angle FAD = angle ACD = 60°

∆ACD is a right triangle.

CD||BE and CD = BE

Again,

∆ ABE is a right triangle.

•To find the value of BC ,we need to substrate AB from AC.

AC = 11 m

BC = AC- AB

So, the height of the lamp post is 7.33 (approx) m.