The angle of depression of the top of a pole, 7 m high from the top of a building in 60° andthe angle of depression of the foot of the building from the top of the pole in 45°. Find theheight of the building and the distance between the building and the pole. please explain the steps
Answers
The height of the building is 19.12 m and the distance between the building and the pole of 7 m high is 7 m.
Step-by-step explanation:
Referring to the figure attached below, we have
The height of the pole, AB = 7 m
The angle of depression of the top of a pole from the top of the building = 60°
The angle of depression of the foot of the building from the top of the pole = 45°
Step 1:
From the figure we can see that
∠ACB = 45° and ∠CAD = 60° ...... [alternate angles]
Let the distance between the building and the pole BC be "x" m.
Consider ΔABC, applying the trigonometry properties of triangles, we have
tan θ = [Perpendicular] / [Base] = AB/BC
⇒ tan 45° = 7/x ..... [here θ = 45°]
⇒ 1 = 7/x
⇒ x = 7 m ← length of BC
Step 2:
Since BC // AD & AB // CD, ∴ AD = BC = 7 m & AB = CD = 7 m
Let's assume ED be denoted as "h" m
Now, consider ΔAED, applying the trigonometry properties of triangles, we have
tan θ = [Perpendicular] / [Base] = ED/AD
⇒ tan 60° = h/7 ...... [here θ = 60°]]
⇒ √3 = h/7
⇒ h = 7√3
⇒ h = 7 * 1.732
⇒ h = 12.12 m
Step 3:
Therefore,
The height of the building is given by,
= ED + CD
= h + 7
= 12.12 + 7
= 19.12 m
Thus, the height of the building is 19.12 m and the distance between the building and the pole is 7 m.
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Answer:
19.12 m height of buliding
and 7m is distance
Step-by-step explanation:
ans is 19.12 m
