2017 · Q53
Let AB represent a building of height h metre with A being its top, B being its bottom. Let A'B' represent a tower of height (h + x) metre (x > 0) with A' being its top and B' being its bottom. Let BB' = d metre. Let the angle of elevation of A' as seen from A be 45° Consider the following statements :
Statement Ih + x > d
Statement IIThe angle of depression of B as seen from A' is less than 45°.
Which one of the following is correct in respect of the above statements ?
Elementary MathematicsTrigonometry
- ABoth Statement I and Statement II are true and Statement II is the correct explanation of Statement I
- BBoth Statement I and Statement II are true but Statement II is not the correct explanation of Statement I
- CStatement I is true but Statement II is false
- DStatement I is false but Statement II is true
Explanation
The angle of elevation of A′ from A has tan = (h+x−h)/d = x/d = tan 45° = 1, so x = d. Then h+x = h+d > d since h > 0 — Statement I is true. The angle of depression of B from A′ has tan = (h+x)/d = 1+h/d > 1, so it exceeds 45° — Statement II (claims < 45°) is false. Hence option (C).