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8.3 Trigonometry

Learn about trigonometric ratios, identities, and their applications in right triangles. Discover how to find side lengths, angle measurements, and distances using trigonometric functions. Explore real-life examples and understand the importance of inverse trig functions.

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8.3 Trigonometry

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  1. 8.3 Trigonometry • Objective – To use the sine, cosine, and tangent ratios to determine side lengths and angle measurements in right triangles • Trigonometric Ratios • Similar right triangles have equivalent ratios for their corresponding sides.

  2. Why???? • Trig identities help us with right triangle geometry when we do not have a 30-60-90 triangle, or a 45-45-90 triangle. We can’t use the Pythagorean theorem because we may only know one side length of the triangle.

  3. Trigonometric Ratios

  4. Using a Trigonometric Ratio to Find Distance • In 1990, the Leaning Tower of Pisa was closed to the public due to safety concerns. The tower reopened in 2001 after a 10-year project to reduce its tilt from vertical. Engineers’ efforts were successful and resulted in a tilt of 5°, reduced from 5.5°. Suppose someone drops an object from the tower at a height of 150 ft. How far FROM the base of the tower will the object land? Round to the nearest foot.

  5. The INVERSE Trig function! • If we have a right triangle, and know the lengths of at least two sides, we can use the INVERSE trig functions to find the measure of the angle

  6. Why do we care? Architecture, engineering, art…. It is useful in these three areas, plus more. Navigators (air and sea) use this to determine the degree of turn they need to make at a particular point (Helmsman! Come 15 degrees to port! Aye Aye – 15 degrees to Port, Sir!)

  7. Hmmmmm… can you prove this?

  8. Exit ticket

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