Trigonometry Skill 41 Objective HSGSRT 78 Students are

Trigonometry Skill 41

Objective HSG-SRT. 7/8: Students are responsible for using sine, cosine, and tangent ratios to determine side lengths and angle measures in right triangles.

Definitions Similar right triangles have equivalent ratios for their corresponding sides called trigonometric ratios.

Trigonometric Ratios Name the sine, cosine, and tangent of angle A. B c A b C

Example 1; Writing Trigonometric Ratios What are the sine, cosine, and tangent of angle T. G 17 T 15 R

Example 1; Writing Trigonometric Ratios What are the sine, cosine, and tangent of angle G. G 17 T 15 R

Example 2; Using Trigonometry to Find Distance a) 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 5ᵒ, reduced from 5. 5ᵒ. 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. The object will land about 13 feet from the tower.

Example 2; Using Trigonometry to Find Distance b) A section of Filbert Street in San Francisco rises at an angle of about 17ᵒ. If you walk 150 ft up this section, what is your vertical rise? Round to the nearest foot. The vertical rise is about 44 feet up.

Example 3; Using Inverses 10 X

Example 3; Using Inverses Y 20

Example 3; Using Inverses Z 100

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