Geometric shape formed by two rays (initial and ending sides of the angle) that share a common endpoint called the vertex. You may name an angle using the vertex, or a point in each ray and the vertex label in the center.
Angle of Elevation is the angle formed by the straight oblique line connecting a point in the horizontal and a point above the horizontal. As viewed by one observer for whose eye the horizontal is drawn.
Angle of depression is the angle formed by the straight oblique line connecting a point in the horizontal and a point below the horizontal. As viewed by one observer for whose eye the horizontal is drawn.
Ratio determined by the hypotenuse in a right triangle and a side adjacent to a reference angle.
The side opposite the right angle in a right triangle.
A statement that two ratios are equal.
One of four numbers that form a true proportion.
Pythagorean theorem a2 + b2 = c2.
The Pythagorean theorem states that if you have a right triangle, then the square built on the hypotenuse is equal to the sum of the squares built on the other two sides.
A quotient of 2 numbers.
Ratio of the length of the opposite side to a reference angle in a right triangle and the hypotenuse. Opposite/hypotenuse.
The ratio of the length of the opposite side of a reference angle to the adjacent side to the same angle. Opposite over adjacent.
Interactive Geometric Applets: Relevant Theorems.
These problems require that besides determining if you have angle of elevation,
or angle of depression: You use sine, cosine, or tangent. This applet will allow you
to review the trigonometric ratios in context to their inverse. All you need to do is to
drag any vertex and view how the values are updated in the table.
Many times in trigonometry you will need to use the Pythagorean Theorem to complete
the solution of the problem. Try this applet by dragging any of the vertices and
verifying that the square of the hypotenuse is equal to the sum of the square of each one
of the legs.
Angles of depression, and elevation may be viewed as alternate interior angles; and therefore
they are congruent. Move point "B" in this applet to view how alternate interior angles are
congruent when the lines are a parallel.
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