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# Trigratios

## by Angelina Pascua Lumbre, Working at Lourdes School Quezon City on Dec 13, 2009

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## TrigratiosPresentation Transcript

• PYTHAGORAS __ __ __ __ __
• Find the message: A famous quotation of Pythagoras is given in the boxes. To find this, cross out the box that does illustrate a property of a right triangle. The remaining boxes will give the quotation. 1. WORLD 2. ABOVE 3. ALL 4. EXACT It has parallel sides. Its acute angles are complementary. The perpendicular sides are the legs. The interior angles are congruent. 5. THINGS 6. REVERENCE 7. CAPACITY 8. OF If c is the hypotenuse, then a 2 +b 2 =c 2 Either legs of a right triangle can serve as the altitude. It has two right angles. If two legs are congruent then all the angles are congruent. 9. OUR 10. TO 11.FUTURE 12. YOURSELF The hypotenuse can be shorter to any of the two legs. The altitude is proportional to the segments of the hypotenuse. The legs a and b can be opposite to the right angle. If two legs of a right triangle are congruent, then it is a 45-45-90 triangle.
• PYTHAGORAS A bove all things , reverence yourself .
• RIGHT TRIANGLE SIMILARITY WAIT.... What are the parts of a right triangle?
• RECALL... E I L
• RIGHT TRIANGLE SIMILARITY G E L M I R
• RATIO OF CORRESPONDING SIDES G E L M I R hypotenuse opposite leg adjacent leg hypotenuse opposite leg adjacent leg
• TRIGONOMETRIC RATIOS... before that... What is trigonometry?
• TRIGONOMETRY derived from the Greek words trigonon and metria , that means measurement of triangles.
• Now lets go back... TRIGONOMETRIC RATIOS
• Let be a right triangle with right angle at E. The sine (sin), cosine (cos), and tangent (tan ) are defined as follows: G E L sin L = = cos L = = tan L = = c a b
• CHECK YOUR UNDERSTANDING... G E L M I R 51 45 24 17 15 8 Compare the sine, cosine and tangent ratios for angles L and R in each triangle below.
• EXAMPLE: 1. Find the value of sin M, cos M, and tan M in the figure below: 2. Using the same figure, find the value of sin R, cos R, and tan R. M I R 12 5
• SYNTHESIS: Help me make this easy!
• Let be a right triangle with right angle at E. The sine (sin), cosine (cos), and tangent (tan ) are defined as follows: G E L sin L = = cos L = = tan L = = c a b
• sin L = = cos L = = tan L = =
• SOHCAHTOA SOHCAHTOA SOHCAHTOA SOHCAHTOA SOHCAHTOA