Here are the essential concepts you must grasp in order to answer the question correctly.
Right Triangle Properties
A right triangle has one angle measuring 90 degrees, and the relationships between the angles and sides are governed by trigonometric ratios. In this problem, the right triangle's height (x) and base (1600) can be analyzed using these properties to find unknown lengths based on known angles.
Recommended video:
Trigonometric Ratios
Trigonometric ratios, such as sine, cosine, and tangent, relate the angles of a triangle to the lengths of its sides. For example, in this triangle, the tangent of the angle can be used to express the height (x) in terms of the base (1600) and the angle (66°), allowing for the calculation of x.
Recommended video:
Introduction to Trigonometric Functions
Angle Relationships in Triangles
The sum of the angles in any triangle is always 180 degrees. In this case, knowing one angle (66°) allows us to find the other angle (24°) since the right angle is 90°. This relationship is crucial for applying trigonometric functions correctly to solve for the unknown side length.
Recommended video: