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1) Find the value of x and y.
2) Then use the Order of Operations to help you out with the computation.
Answer: the distance of the boat from the foot of the lighthouse is 290.5 feet.
Step-by-step explanation:
The right angle triangle ABC representing the scenario is shown in the attached photo.
Angle A is alternate to the angle of depression, hence, they are the same.
The height of the lighthouse represents the opposite side of the right angle triangle. The distance, x of the boat from the foot of the lighthouse represents the adjacent side of the right angle triangle.
To determine x, we would apply
the tangent trigonometric ratio.
Tan θ, = opposite side/adjacent side. Therefore,
Tan 11.1 = 57/x
x = 57/Tan 11.1 = 57/0.1962
x = 290.5 feet to the nearest tenth.
Triangles CPA and CPB are both right triangles. They share a leg, so that leg in one triangle is congruent to that leg in the other triangle. We are given that PA is congruent to PB by the hash marks on the diagram. Thus two legs and an included angle are congruent between the triangles.
... ∆CPA ≅ ∆CPB by the SAS postulate
Then side CA ≅ CB = 15 in, because corresponding parts of congruent triangles are congruent (CPCTC).
... CA is 15 in.
Answer:
y = 17x
Step-by-step explanation: