Similar to an angle of elevation, an angle of depression is...

Similar to an angle of elevation, an angle of depression is the acute angle formed by a horizontal line and an observer's line of sight to an object below the horizontal. A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, $6.6 \mathrm{km}$ apart, to be $37^{\circ}$ and $44^{\circ},$ as shown in Figure 32. Find the distance of the plane from point $A$ to the nearest tenth of a kilometer.

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Key Concepts

Tangent Function

The tangent function in trigonometry is defined as the ratio of the opposite side to the adjacent side in a right triangle. It is crucial to this type of problem because the angles of depression, when translated into the geometry of the scenario, lead directly to the use of the tangent ratio to relate the height of the plane to the distances on the highway.

Angle of Depression

The angle of depression is the acute angle formed between a horizontal line and the line of sight looking downward to an object. It is fundamental in problems involving heights and distances because it allows the use of trigonometric ratios in right triangles by relating the vertical height and horizontal distance between the observer and the object.

Right Triangle Trigonometry

Right triangle trigonometry is the study of the relationships between the angles and sides of a right-angled triangle. In the context of this problem, it is used to set up equations relating the height of the plane to the horizontal distances from the points on the ground, which are determined by the angles of depression observed by the pilot.

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