θ hypotenuse adjacent opposite There are 6 trig ratios that can be formed from the acute angle θ. Sine θ= sin θCosecant θ= csc θ Cosine θ= cos θSecant θ= sec θ Tangent θ= tan θCotangent θ= cot θ θ hypotenuse opposite adjacent The opposite and adjacent sides change depending on which acute angle you use.

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 = 41 0, 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 b? How could we find B?

Solving Right Triangles Question 1 C A B c b a Lets say A = 41 0, 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, but since the calculator only has sine, cosine, and tangent you have to change cot41 to 1/tan41, depending on the type of calculator you have.

Solving Right Triangles question 2 C A B c b a What trig ratio(s) could we use to find side b? How could we find B? You can use either of these to find c, but again sec will have to be typed in as 1/cos, again depending on your calculator.

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 = 49 0 A = 41 0 B= 49 0 a = cm, b = 12.5 cm, c = cm

Solving Right Triangles C A B c b a Lets try another example B = , 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 Next I am going to use cosine to find a.Last I am going to use sine to find b. A = , a = 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 b 2 = 50 2 b 2 = 736, b = Next I am going to use sine to find A.Last I am going to find B by subtracting A from 90. B = 90 – = When finding an angle you have to use the 2 nd sine to get the decimal to change to an angle. A = B = , b = inches

C A B c b a #1) c = 10, A = 40 0 find b, a, and B

A ladder is leaning against the wall of a house the angle at which it touches the house is 22 0 if the foot of the ladder is 5.2 feet from the house. How tall is the ladder? 5.2 feet 22 0 Sin 22 0 = 5.2/x x(sin 22 0 ) = 5.2 x = 5.2/sin22 0 x = feet

#2) A 22 foot ladder leaning against a building makes a 70 0 angle with the ground. How far up the building does the ladder reach?