From a boat on the lake, the angle of elevation to the top of a cliff is 26°1'. If the base of the cliff is 205 feet from the bo
at, how high is the cliff (to the nearest foot)?
2 answers:
We use the tangent for this
tan 26 1 = opposite / adjacent = h / 205 where h = height of cliff
h = 205 tan 26 1 = 100 feet
Answer:
Let the distance of the cliff from the boat be y and height of the top of the cliff be x.
As per the statement:
From a boat on the lake, the angle of elevation to the top of a cliff is 26°1'. If the base of the cliff is 205 feet from the boat.
⇒y = 205 feet,
We have to find the high is the cliff i,e x.
Using tangent ratio:
See the diagram as shown below:
Opposite side = x feet
adjacent side = 205 feet
Using conversion:
then;
Substitute these values we have;
Multiply both sides by 205 we have;
ft
Therefore, 100 ft high is the cliff(to the nearest foot)
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