Question

Two vertical cliffs are on opposite sides of a 90 foot wide river. From point A at the top of the shorter cliffs, the angle of elevation of the top of the other cliff (B) is 28 degrees and the angle of depression to the bottom is 38 degrees. Find the height of each cliff, to the nearest foot.

Answer 1

Hope it helps..........

Answer 2

Answer:

Height of longer cliff is 118.16 feet

Height of shorter cliff is 70.3157 feet

Step-by-step explanation:

Refer the attached figure .

In ΔABC

$Tan \theta = \frac{Perpendicular}{Base}$

$Tan 38^{\circ} = \frac{AB}{BC}$

$Tan 38^{\circ} = \frac{AB}{90}$

$90 \times Tan 38^{\circ} =AB$

$70.3157 =AB$

Height of shorter cliff is 70.3157 feet

In ΔADE

$Tan \theta = \frac{Perpendicular}{Base}$

$Tan 28^{\circ} = \frac{DE}{AD}$

$Tan 28^{\circ} = \frac{DE}{90}$

$90 \times Tan 28^{\circ} =DE$

$47.853 =DE$

Height of longer cliff = DE+EC=70.3157+47.853=118.16

Thus height of longer cliff is 118.16 feet