The angle of depression is the angle formed with the horizontal, when an object is viewed below the horizontal level. Thus, the height of the cliff is approximately 123.86 m.
Let the height of the cliff be represented by h, so that:
From the triangle 1, we have:
tan [tex]32^{o}[/tex] = [tex]\frac{h}{x}[/tex]
⇒ h = tan [tex]32^{o}[/tex]*x
h = x tan [tex]32^{o}[/tex] ............. 1
Also, from the bigger triangle, we have:
tan [tex]24^{o}[/tex] = [tex]\frac{h}{80 + x}[/tex]
⇒ h = tan [tex]24^{o}[/tex] (80 + x) ......... 2
Now equating the expressions for h in equations 1 and 2, we have:
x tan [tex]32^{o}[/tex] = tan [tex]24^{o}[/tex] (80 + x)
0.6249x = 0.4452 (80 + x)
= 35.616 + 0.4452x
0.6249x - 0.4452x = 35.616
0.1797 x = 35.616
x = [tex]\frac{35.616}{0.1797}[/tex]
x = 198.2 m
Substitute the value of x in equation 1;
h = x tan [tex]32^{o}[/tex]
= 198.2 * 0.6249
= 123.8552
h = 123.86 m
Therefore, the height of the cliff is approximately 123.86 m.
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