From the top of a house A in a street, the angles of elevation and depression of the top and foot of another house B on the opposite side of the street are $$60^\circ$$ and $$45^\circ$$, respectively. If the height of house A is 36 m, then what is the height of house B? (Your answer should be nearest to an Integer.)

From the above question, we draw the diagram is given below 

In $$ \triangle ADC $$

$$ \tan 45^\circ = \frac{DC} {AD} $$

$$ \Rightarrow 1 = \frac{36} {AD}$$

$$\Rightarrow AD = 36 m $$

In $$\triangle ADB $$

$$ \tan 60^\circ = \frac{BD}{AD}$$

$$ \Rightarrow BD= 36 \times \sqrt {3} $$ 

then Length of Building = BD + DC 

              $$ \Rightarrow 36  \sqrt{3} + 36 $$

             $$\Rightarrow 36 (1+\sqrt{3}) $$

             $$ \Rightarrow 36 \times (1+1.73) $$

             $$\Rightarrow 36 \times 2.73 $$

            $$\Rightarrow 98.28 $$

therefore Height of house B= 98 m Ans