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AB C D Clickers x

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AB C D x

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Today we’re going to be working with some special right triangles that occur within other geometric figures The ratios shown today will reappear throughout your odyssey throughout mathematics…

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There are two special right triangles that occur naturally and are thus often studied in trigonometry. We’re going to look at one today and the other on Monday This kind of isosceles triangle is called a 45-45-90 triangle because of the angles formed when you draw a diagonal across a square What’s the length of the diagonal of a square of side length 1 1 1

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How would this relate to triangles whose sides are larger than 1? Therefore the relationship between sides and hypotenuse this triangle is by radical two… 5 5

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Theorem 7.8 In a 45-45-90 triangle, the hypotenuse is radical 2 times as long as each leg

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Solve for x

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This kind of triangle is called a 30-60-90 triangle because of the angles formed when you draw an altitude in an equilateral triangle Given an equilateral triangle of side length 2, can we determine the height of the triangle 1 2 2 h

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How would this relate to triangles whose sides are larger than 1? Therefore the relationship the 60 o side and hypotenuse is one half and the other side is by radical three 3 6 6 h

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Theorem 7.9 In a 30-60-90 triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is √3 times as long as the shorter leg. 30 o 60 o

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Solve for x

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Solve for x & y

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Solve for x

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Solve for x & y

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7.4 Worksheet

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The distance from Bill’s feet to his waist is 3 feet. While doing leg lifts at track practice, he wonders how high his feet are off the ground in order to get his mind off the burning pain in his abs. How far off the ground are his feet when his legs make a 30 o angle with the ground? A.1.5 ft B.2.60 ft C.5.20 ft

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The distance from Bill’s feet to his waist is 3 feet. While doing leg lifts at track practice, he wonders how high his feet are off the ground in order to get his mind off the burning pain in his abs. How far off the ground are his feet when his legs make a 45 o angle with the ground? A.2.12 ft B.3 ft C.4.24 ft

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The distance from Bill’s feet to his waist is 3 feet. While doing leg lifts at track practice, he wonders how high his feet are off the ground in order to get his mind off the burning pain in his abs. How far off the ground are his feet when his legs make a 60 o angle with the ground? A.1.5 ft B.2.60 ft C.5.20 ft

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45-45-90 triangle side relationships45-45-90 triangle side relationships 30-60-90 triangle side relationships30-60-90 triangle side relationships

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EXAMPLE 3 Use a geometric mean Find the value of y. Write your answer in simplest radical form. SOLUTION STEP 1 Draw the three similar triangles.

EXAMPLE 3 Use a geometric mean Find the value of y. Write your answer in simplest radical form. SOLUTION STEP 1 Draw the three similar triangles.

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