the angle of elevation of the top of an unfinished vertical building on the level ground at a point which is hundred metre from the base of the building is 45degree how much height the building must be raised so that its angle of elevation from the same point A 60 degree root 3 equal to 1.73
Answers
In order to have the angle of elevation from point of 100 m from the building be 60 degree, the height of the building must be resized to 173 m.
Step-by-step explanation:
Referring to the figure attached below, we have
The distance of the point C (angle of elevation point) from the base of building, BC = 100 m
The angle of elevation to the unfinished part of the vertical building = 45°
Let the height of the unfinished vertical building be BD = “h” m and the height of the building after being resized be AB = “(h+x)” m
Applying trigonometry property of triangles in ∆ BDC, we get
tanθ = perpendicular /base = BD/BC
⇒ tan 45° = h/100
⇒ 1 = h/100
⇒ h = 100 m …… (i)
We are given that the angle of elevation is shifted to 60 degrees
So, by applying trigonometry property of triangles in ∆ ABC, we get
tanθ = AB/BC
⇒ tan 60° = h+x/100
⇒ √3 = (100+x)/100 ……. [substituting from (i)]
⇒ 100√3 = (100+x)
⇒ x = 100 (√3 - 1)
⇒ x = 100 (1.73 -1)
⇒ x = 100 * 0.73
⇒ x = 73 m
∴ Height of the building now will be = h+x = 100 + 73 = 173 m
Thus, the height of the building must be resized to 173 m, so that its angle of elevation from same point be 60°.
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