The angle of elevation of the top of a vertical pole as seen...

Name: Problem 35, Chapter 8: Higher Level Mathematics
Uploaded: 2020-04-22T17:48:16-08:00
Duration: 3 min 49 s
Channel: Julian Wong
Description: The angle of elevation of the top of a vertical pole as seen from a point 10 metres away from the pole is double its angle of elevation as seen from a point 70 metres from the pole. Find the height (to the nearest tenth of a metre) of the pole above the level of the observer's eyes.

The angle of elevation of the top of a vertical pole as seen from a point 10 metres away from the pole is double its angle of elevation as seen from a point 70 metres from the pole. Find the height (to the nearest tenth of a metre) of the pole above the level of the observer's eyes.

Key Concepts

Angle of Elevation

The angle of elevation is the angle formed between the horizontal line of sight and the line passing through an object’s top. It is a fundamental concept in trigonometry used to model and solve problems involving heights and distances in right triangles.

Tangent Function

In a right triangle, the tangent of an angle is defined as the ratio of the opposite side to the adjacent side. This concept is particularly useful for modeling situations where the height of an object and the horizontal distance from the observer are known or need to be determined.

Double Angle Relationship

When one angle is stated to be twice another, the relationship can be expressed using double angle formulas in trigonometry. For the tangent function, the formula tan(2?) = (2 tan?) / (1 ? tan²?) is often used to connect the angles, thereby facilitating the formation of equations to solve for unknown quantities.

Mathematical Modeling of Geometric Situations

Setting up equations based on geometric representations of physical situations involves translating verbal descriptions into mathematical expressions. In these problems, distances and angles of elevation form right triangles that can be modeled using trigonometric ratios. The resulting equations capture the relationships among the variables, which can then be manipulated algebraically to solve for an unknown such as height.

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