Question

find the angle of depression from point a to point c. angle of depression = ?°

Explanation:

Step1: Use the property of alternate - interior angles

Since the line of sight (horizontal line at \(A\)) is parallel to \(BC\), the angle of depression from \(A\) to \(C\) is equal to the angle \(∠C\) in right - triangle \(ABC\).
In right - triangle \(ABC\), we know that \(\tan C=\frac{AB}{BC}\), and also, using the fact that the sum of angles in a right - triangle \(ABC\) (\(∠B = 90^{\circ}\)): \(∠C+∠BAC = 90^{\circ}\) (because \(∠B = 90^{\circ}\) and \(∠A+∠B + ∠C=180^{\circ}\)).

Step2: Calculate the angle

We know that \(∠BAC = 55^{\circ}\). Let the angle of depression be \(x\).
Since \(x = ∠C\) (alternate - interior angles) and \(∠C+55^{\circ}=90^{\circ}\) (complementary angles in right - triangle \(ABC\)).
Then \(x=90^{\circ}-55^{\circ}\)

Answer:

\(35^{\circ}\)