Question

The angle of depression from the top of the building A to the tortoise is 60°. The angle of elevation from the top of building A to the top of building B is 30°. What is the ratio of the heights of building A is to
building B? (Height of the tortoise is negligible.)​

Answer 1

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Answer 2

Step-by-step explanation:

Given: The angle of depression from the top of the building A to the tortoise is 60°. The angle of elevation from the top of building A to the top of building B is 30°.

To find: What is the ratio of the heights of building A is to building B? (Height of the tortoise is negligible).

Solution:

Draw the figure according to given situation.

See attached figure.

In ∆ABC

$tan \: 60° = \frac{AC}{AB} \\ \\ \sqrt{3} = \frac{AC}{AB} ...eq1$

In ∆CDE

$tan \: 30° = \frac{DE}{CE} \\ \\ \frac{1}{ \sqrt{3} } = \frac{DE}{CE} \\ \\ or \\ \\ \frac{1}{ \sqrt{3} } = \frac{DE}{AB} ...eq2$

(because AB =CE)

Compare both AB from eq1 and eq2

$\sqrt{3} DE = \frac{AC}{ \sqrt{3} } \\ \\ 3DE = AC$

because AC=BE

Height of building B is BD=BE+ED

and AC=BE

Thus,

BD=AC+ED

BD=3DE+DE=4DE

Thus,

$\frac{AC}{BD} =\frac{3DE}{4DE}\\\\\frac{AC}{BD} =\frac{3}{4}$

Final answer:

Height of building A:Height of building B=3:4

Hope it helps you.

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