Apply the Tangent Ratio Chapter 7.5

Trigonometric Ratio A trigonometric ratio is a ratio of 2 sides of a right triangle. You can use these ratios to find sides lengths and angle measures.

Sides of a right triangle Opposite – the side opposite the angle you are looking at.

Sides of a right triangle Adjacent – the side next to the angle you are looking at.

Sides of a right triangle Hypotenuse – the side opposite the right angle. It is also the longest side on a triangle.

Which side does the 22 represent? The hypotenuse, adjacent, or opposite?

Which side is which?

Tangent The ratio that we’ll focus on today is the tangent. The tangent is the opposite side over the adjacent side.

Find the tangent of ŸR and ŸS To find the measure of the angle R, find the tangent. On a scientific calculator use the inverse tangent button to calculate the angle measure.

Find the tangent of ŸJ and ŸK

Find the Tangent of ŸA and ŸB, then the angle measures. Tan A = 0.75 Tan B = m óA = 36.87ô m óB = 53.12ô Tan A = 1.05 Tan B = 0.95 m óA = 46.4ô m óB = 43.5ô Tan A = Tan B = 2.4 m óA = 22.62ô m óB = 67.38ô Tan A = 3.43 Tan B = 0.29 m óA = 73.75ô m óB = 16.17ô Tan A = 1.61 Tan B = m óA = 58.15ô m óB = 31.88ô

Finding missing side lengths Some problems may require you to find a missing side length. In these problems you will be given a side length and a measure of an angle. You will then use the fact that the tangent of an angle is equal to the opposite side over the adjacent side to find the angle.

Example Multiply both sides by the denominator!

Example Multiply both sides by the denominator!

Example Multiply both sides by the denominator!

Example Multiply both sides by the denominator! Divide both sides by the tangent!

Example Multiply both sides by the denominator! Divide both sides by the tangent!

Example Multiply both sides by the denominator! Divide both sides by the tangent!

Example Multiply both sides by the denominator! Divide both sides by the tangent!

Find the length of x for each problem X = 8.66 X = X = X = 25

Tangents and “Special Right Triangles” Recall that for a triangle the side lengths are: – leg = x-or- leg = 1 – Hypotenuse = x-or- Hypotenuse = Recall that for a triangle the side lengths are: – Shorter leg = x-or- Shorter leg = 1 – Longer leg = x-or- Longer leg – Hypotenuse = 2x -or- Hypotenuse =2

What length must x be?

What must x be?

A little more abstract… If I tell you that a right triangle has a measure of 30 degrees, could you find the tangent of the angle?

A little more abstract… If I tell you that a right triangle has a measure of 45 degrees, could you find the tangent of the angle?