Question

From a boat on the lake, the angle of elevation to the top of a cliff is 15°54'. If the base of the cliff is 967 feet from the boat how high is the cliff to the nearest foot?

Answer 1

Answer:

Height of the cliff is 188 feet.

Step-by-step explanation:

Let us draw a diagram for the given situation.

In the diagram,

AB = cliff with base at B

C is the position of boat.

Hence, BC = 967.

∠C = 15°54' = 15.9°

In triangle ABC, we have

$\tan C=\frac{AB}{BC}\\\\\tan 15.9=\frac{x}{967}\\\\x=967\tan 15.9\\\\x=188.01$

Hence, in nearest foot, the height of the cliff is 188 feet.

Answer 2

Tan 15 54 = h  / 967

h = 967  * tan 15 54

=  275 feet to nearest foot