9.5 Trigonometric Ratios

Advanced Geometry

TRIGONOMETRIC RATIO

A trig ratio is a ratio of the lengths of two sides of a right triangle. There are three basic trig ratios:

sine cosine tangent sin cos tan

SINE

COSINE

TANGENT

Find sin, cos, and tan of A

Example

Compare the sine, the cosine, and the tangent ratios for angle A in each triangle below.

Example

Find the sine, the cosine, and the tangent of angle D and angle E.

Use A Calculator

Use a calculator to approximate the sine, cosine, and tangent of 82 degrees.

Use a Calculator

Use a calculator to approximate the sine, cosine, and tangent of 54 degrees.

Note:

Sin and Cos must always be less than 1!!

Using Trig to find lengths

Using Trig to find lengths

Using Trig to find lengths

ANGLE OF ELEVATION

The angle that your line of sight makes with a line drawn horizontally is called the angle of elevation.

Example

You are measuring the height of a building. You stand 100 feet from the base of the building. You measure the angle of elevation from a point on the ground to the top of the building to be 48 degrees. Estimate the height of the building.

Example

A driveway rises 12 feet over a distance d at an angle of 3.5 degrees. Estimate the length of the driveway.

Example

The angle of elevation from the base to the top of a waterslide is about 13 degrees. The slide extends horizontally about 58.2 meters. Estimate the height of the slide.

Example

Your family room has a sliding-glass door with a southern exposure. You want to buy an awning for the door that will be just long enough to keep the sun out when it is at its highest point in the sky. The angle of elevation of the sun at this point is 70°, and the height of the door is 8 feet. About how far should the overhang extend?