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In this example, we use angles of elevation to find the height of a flagstaff atop a 10 m building and the distance from a point on the ground to the building. Utilizing right triangles and the tangent function, we derive both measurements.
In this section, Example 4 illustrates a practical application of trigonometry using angles of elevation to find unknown distances and heights. Starting with a point P on the ground, where the angle of elevation to the top of a 10 m tall building (AB) is measured at 30°, the distance from point P to the building's base (PA) is calculated using the tangent function. Subsequently, the height of a flagstaff positioned atop the building (BD) is determined with the angle of elevation to the flag's top (AD) measured at 45°. By creating two right triangles, the solution employs the relationships of tangent and height to arrive at the required distances. The example emphasizes the practical use of trigonometry in real-life scenarios.
Angle of Elevation: The angle between the horizontal line and the line of sight to an object above.
Tangent Function: A crucial concept in trigonometry representing the ratio of the opposite side over the adjacent side in a right triangle.
Opposite and Adjacent Sides: Terms that describe the relationship between the sides of a right triangle in relation to a specific angle.
Up to the sky, the angle is nigh, check the height from the ground, let it be found!
Once, a student looked up at a tall building, curious about its height. With a straight line of sight, they measured the angle, finding the distant ground, creating triangles in the air.
H-O-A: Height over Adjacent for Tangent’s game!
Using a 10 m tall building, with an angle of elevation of 30°, we find the distance from point P to the building.
From the same point, with a 45° angle of elevation to the flagstaff atop the building, we calculate the flagstaff's height.
Term: Angle of Elevation
Definition: The angle formed between the horizontal line from the observer and the line of sight to a point above.
The angle formed between the horizontal line from the observer and the line of sight to a point above.
Term: Tangent Function
Definition: A trigonometric function defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.
A trigonometric function defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.
Term: Opposite Side
Definition: In a right triangle, the side opposite the angle of interest.
In a right triangle, the side opposite the angle of interest.
Term: Adjacent Side
Definition: In a right triangle, the side adjacent to the angle of interest.
In a right triangle, the side adjacent to the angle of interest.
Term: Right Triangle
Definition: A triangle where one of the angles is a right angle (90 degrees).
A triangle where one of the angles is a right angle (90 degrees).