Answer:
Cliff is 45 m tall.
Step-by-step explanation:
Given:
Height of Sarah = 1.8 m
Angle of elevation = 60°
Angle of elevation 50 m back = 30°
As shown in the figure we have two right angled triangles SPQ and SPR.
Let the height of the cliff be meters and
.
Using trigonometric ratios:
tan (Ф) = opposite/adjacent
In ΔSPQ. In ΔSPR.
⇒ ...equation (i) ⇒
...equation (ii)
Dividing equation (i) and (ii)
⇒
⇒
⇒
⇒
⇒
⇒
⇒ meters
To find plugging
in equation (i)
⇒
⇒
⇒ meters
The height of the cliff from ground :
⇒
⇒
⇒ meters
The cliff is 45 m tall to the nearest meter.
