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hypotenuseadjacentoppositeThere are 6 trig ratios that can be
formed from the acute angle .
Sine = sin Cosecant = csc Cosine = cos Secant = sec Tangent =
tan Cotangent = cot hypotenuseoppositeadjacent
The opposite and adjacent sides change depending on which acute
angle you use.
Solving Right TrianglesWe 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.CABcbaBefore going on any farther try answering these
questionsLets 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
b?How could we find B?Solving Right Triangles Question 1CABcbaLets
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, 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 2CABcbaWhat 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 3CABcbaHow 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 = 490A = 410 B= 490 a =
10.87 cm, b = 12.5 cm, c = 16.56 cmSolving Right
TrianglesCABcbaLets try another example B = 18.80, and c = 42.5
yard. We need to find A, a, and bWhat would you find first?I am
going to find A first by taking 90 18.8 and get 71.20Next 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
TrianglesCABcbaLets try another example a = 42 inches, and c = 50
inches. We need to find A, B, and bWhat would you find first?I am
going to find b first by using Pythagorean Theorem. 422 + b2 =
502b2 = 736, b = 27.13Next 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
= 32.860When 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
inchesPractice timeCABcba#1) c = 10, A = 400 find b, a, and BA
ladder is leaning against the wall of a house the angle at which it
touches the house is 220 if the foot of the ladder is 5.2 feet from
the house. How tall is the ladder?
Application problems:5.2 feet 220Sin 220 = 5.2/xx(sin 220) =
5.2x = 5.2/sin220x = 14.682 feetPractice time#2) A 22 foot ladder
leaning against a building makes a 700 angle with the ground. How
far up the building does the ladder reach?