Sarah’s stands on a ground and sights the top of a steep Clift at a 60 degree angle of elevation she then steps back 50 meters then sights the top of the steep cliff at a 30 degree angle if Sarah is 1.8 meters tall how tall is the cliff to the nearest meter ?

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.

5

step-by-step explanation: