Trigonometry Advanced Geometry Trigonometry Lesson 3.

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Presentation transcript:

Trigonometry Advanced Geometry Trigonometry Lesson 3

Parts of a Right Triangle acute angle acute angle hypotenuse opposite leg adjacent leg opposite leg adjacent leg hypotenuse – the side of a right triangle opposite the right angle adjacent leg – the leg of a right triangle that is also a side of the given acute angle opposite leg – the leg of a right triangle that is not also a side of the given acute angle

Sine Ratio Abbreviated: sin hypotenuse opposite leg

Cosine Ratio Abbreviated: cos hypotenuse adjacent leg

Tangent Ratio Abbreviated: tan opposite leg adjacent leg

Example: Use ∆ ABC with right angle C to find sin A, cos A, tan A, sin B, cos B, and tan B. Express each ratio as a fraction, and as a decimal to the nearest hundredth. AB = 17, BC = 15, and AC = 8 Write the Ratio Problems

Examples: Use a calculator to find each value. Round to the nearest ten-thousandth. tan 56ºcos 89º Find the Value Problems

In problems where either an angle OR side measure is missing, set up a trigonometric ratio as shown below. tan Missing Measure Problems Ratio Name of the Trig. Ratio Angle Measure or variable = 47=

Examples: Find x. Round to the nearest tenth.

Examples: Find x. Round to the nearest tenth.

Examples: Find x. Round to the nearest tenth.

Example: A fitness trainer sets the incline on a treadmill to 7º. The walking surface is 5 feet long. Approximately how many inches did the trainer raise the end of the treadmill from the floor?

Example: Find x and y. Round to the nearest tenth.