Solving Right Triangles

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Presentation transcript:

Solving Right Triangles We have learned about the ratios for the six trig functions, so what can we do with these? Well we can use them to find missing angles and sides for any right triangle. As long as we know 2 of the parts to the trig ratio we can find the third part. For example if we know an acute angle and the opposite side we could use sine or cosecant to find the hypotenuse and we could use tangent or cotangent to find the adjacent side. C A B c b a Before going on any farther try answering these questions Lets say A = 410, and b = 12.5 cm what trig ratio(s) could we use to find side a? What trig ratio(s) could we use to find side c? How could we find B?

Solving Right Triangles Question 1 C A B c b a Lets say A = 410, and b = 12.5 cm what trig ratio(s) could we use to find side a? You can use either of these to find a.

Solving Right Triangles question 2 C A B c b a What trig ratio(s) could we use to find side c? How could we find B?

Solving Right Triangles question 3 C A B c b a How could we find B? Sum of the 3 angles of a triangle add to equal 180 and since one angle is 90 the other 2 must add to equal 90. B = 90 – 41 = 490 A = 410 B= 490 a = 10.87 cm, b = 12.5 cm, c = 16.56 cm

Solving Right Triangles C A B c b a Lets try another example B = 18.80, and c = 42.5 yard. We need to find A, a, and b What would you find first? I am going to find A first by taking 90 – 18.8 and get 71.20 Next I am going to use cosine to find a. Last I am going to use sine to find b. A = 71.20, a = 40.23 yards, b = 13.7 yards.

Solving Right Triangles C A B c b a Lets try another example a = 42 inches, and c = 50 inches. We need to find A, B, and b What would you find first? I am going to find b first by using Pythagorean Theorem. 422 + b2 = 502 b2 = 736, b = 27.13 Next I am going to use sine to find A. Last I am going to find B by subtracting A from 90. B = 90 – 57.14 = 32.860 When finding an angle you have to use the 2nd sine to get the decimal to change to an angle. A = 57.140 B = 32.860, b = 27.13 inches

Practice time #37) c = 9, B = 200 find b, a, and A C A B c b a

Assignment# Pg. 516-517 9-18 by 3’s 29-41 odds