Angles of Elevation and Depression in Right Trigonometry with Sine, Cosine, and Tangent Ratios.

There you are with your homework: Problems with angle of elevation, and depression. How I need to apply the angle? From the wall, or from the horizontal? Will I need angle of elevation, or angle of depression? Once, I decided what angle to consider; what should I use? Sine, or Tangent? ...Maybe cosine!

You will find this lesson to be a relief for you. It addresses the answers to all of the above considerations. It will stress the reading process of each one of the problems, and it will include diagrams, and drawings to help you and guide you through the whole problem solving process. This is your lesson, use it!

Lesson's Content

Lesson's Glossary

Angle
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.

Cosine
Ratio determined by the hypotenuse in a right triangle and a side adjacent to a reference angle.

Hypotenuse
The side opposite the right angle in a right triangle.

Proportion
A statement that two ratios are equal.

Proportional
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.

Ratio
A quotient of 2 numbers.

Sine
Ratio of the length of the opposite side to a reference angle in a right triangle and the hypotenuse. Opposite/hypotenuse.

Tangent
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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