Solving trigonometry problems for right triangles to find sides and angles using sine, cosine and tangent.

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.

Sine is defined as opposite leg over hypotenuse; cosine is adjacent leg over hypotenuse;

and tangent is opposite leg over adjacent leg. This applet will allow you to verify these

relationships in a dynamic way. You will be able to drag any of the vertices in the

triangle to view how the values in the table are updated. It allows you to verify the

difference and similarity between a trigonometry ratio and its inverse.

Once you have found one leg, and the hypotenuse, or both legs you may use the Pythagorean

Theorem to find the missing side in the triangle. This applet will allow you to play with

any of the vertices, and verify how the theorem holds true. Observe that the red, and green

areas of the square at the legs fits in the square of the hypotenuse.

In a triangle, when you have found two angles, then you may use the Angle Sum Theorem

to find the remaining angle. This applet allows you to drag any vertex, and verify that the

sum of the three angles is always 180°.

Right Triangle Trigonometry: Sine, Cosine, and Tangent Ratios. Solution of Problems.

We really try to give you the easiest way of answering all those questions. The presentation of concepts and solution of problems privilege animations, sequence, and colors over long paragraphs difficult to understand. You will feel very supported all along the lesson!