Discussion
Guddi was standing on a road near a mall. She was 1000m away from the mall and able to see the top of the mall from the road in such a way that top of the tree, which is in between her and the mall, was exactly in line of sight with the top of the mall. The tree height is 10m and it is 20m away from Guddi. How tall is the mall?
Answer: C
Guddi's eye, the top of the tree and the top of the mall lie on one straight line, so the tree and the mall are the vertical sides of two similar right triangles sharing the apex at Guddi.
\[ \frac{\text{tree height}}{\text{distance to tree}} = \frac{\text{mall height}}{\text{distance to mall}} \]
\[ \frac{10}{20} = \frac{H}{1000} \]
\[ H = 1000 \times \frac{10}{20} = 1000 \times 0.5 = 500 \text{ m} \]
The 1000 m is measured from Guddi, not from the tree, so it is the full base of the larger triangle - using 980 m here is the usual slip.
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