Chapter 7.5 Notes: Apply the Tangent Ratio

Goal: To use the tangent ratio to determine side lengths in triangles.

Using the Tangent Ratio:

A trigonometric ratio is a ratio of the lengths of two sides in a right triangle.

You will use trigonometric ratios to find the measure of a side.

The ratio of the lengths of the legs in a right triangle is constant for a given angle measure. This ratio is called the tangent of the angle.

Ex.1: Find tan S and tan R. Write each answer as a fraction and as a decimal rounded to four decimal places.

Ex.2: Find tan J and tan K. Round to four decimal places.

• Find the value of x. Round to the nearest tenth, if necessary.

Ex.3: Ex.4:

Ex.5: Find the height h of the lamppost to the nearest inch.

Ex.6: A surveyor is standing 118 feet from the base of the Washington Monument. The surveyor measures the angle between the ground and the top of the monument to be 78o. Find the height, h, of the Washington Monument to the nearest foot.

Ex.7: Find the value of x. Round to the nearest tenth, if necessary.

Ex.8: Find the value of x. Round to the nearest tenth, if necessary.

9

17o

x

Ex.9: Find the tangent of a 60o angle.