Trig Ratios
What is the trig ratio sine?
Sine = opp/hyp
Triangle ABC has a right angle at angle B.
a=8, b=17,c=15
Find the ratio of CosA.
15/17
The sum of the interior angles of a triangle is?
180 degrees
True or False? You can only use the Law of Sines on a non right triangle.
False. You can use it on a right triangle, however, it is extra work than using the trig ratios.
True or False? You can only use the Law of Cosines with a non right triangle.
False. You can use it on a right triangle, however, it is extra work than using the trig ratios.
What is the trig ratio cosine?
Cosine = adj/hyp
Solve for x. Round to the nearest tenth.
sin 38 = 14/x
22.7
In a right triangle, one of the angles is 37 degrees. What are the measures of the other two angles individually?
90 degrees and 53 degrees
True or False? You only need to use the inverse function button when solving for a missing angle.
True
True or False? There are 2 versions of the cosine formulas, one that solves for the length of a triangle and one that solves for a missing angle measure.
True
What is the trig ratio tangent?
Tangent = opp/adj
Solve for B. Round to the nearest degree.
tanB=18/13
m<B=54 degrees
What are the trig ratios used for?
Solving for an unknown side length or angle measure in a right triangle.
What does the Law of Sines formula look like?
Sin A/a = Sin B/b = Sin C/c
What is the Law of Cosines Formula?
a2 = b 2 + c 2 - 2bcCosA
b2 = a 2 + c 2 - 2acCosB
c2 = a 2 + b 2 - 2abCosC
The trig ratios of sine theta, cosine theta and tangent theta are used with what type of a triangle?
Right triangle.
Solve for A. Round to the nearest degree.
sin(70) / 16 = sin(A) / 9
m<A=32 degrees
What phrase is used to remember the trig ratios? (mneumonic)
SohCahToa
What did we draw to prove the Law of Sines?
A line that connects one vertex with its opposite side at a right angle.
When do you use Law of Cosines rather than Law of Sines on a non-right triangle?
When you do NOT have an angle-side pair
True or False? You can use any trig ratio to solve any triangle problem.
False
Law of Cosines: Solve for C. Round to degree. (^2 is squared)
12^2=3^2+10^2-2(3)(10)cosC
m<C=126 degrees
What options do we have to solve for missing sides and angles if the triangle is NOT a right triangle?
Law of Cosines
When do we have multiple solutions?
When the opposite side is bigger than the vertical height but smaller than the adjacent side.
Please provide two examples of what we can be given and we would use the Law of Cosines. (Hint: NOT Angle-Angle-Side)
1. two side lengths and an angle between them is given. (SAS)
2. three side lengths are given. (SSS)