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85°-35°=50°
35°
180°-135° = 45°
135°
85°
Hypotenuse
Opposite
Can add or subtract angles to find missing angles of the same corner.
All angles of a Triangle <A+<B+<C = 180°
Pythagorean Theorem
a² + b² = c²
90°
X
Adjacent
Usually one of the simpler triangles so solve. Formulas are simple and the 90° is always given
Trigonometry
Oblique Triangle
Right Angle Triangle
Triangles that have a Right Angle Corner
These triangles can be the standard look for triangles or distorted to all angles as long as it doesn't have a right angle to it
Solving
Sine = Opposite/Hypotenuse
Cosine = Adjacent/Hypotenuse
Tangent = Opposite/Adjacent
If you have 3 Sides but no angles you find out an angle
Can Use Sine, Cosine and Tangent formulas to solve. Commonly known as SohCahToa
If the Angle is given the equation can be rewritten to solve for a side.
Hyp = Opp/Sine or Opp=Sine x Hyp
Solving Oblique Triangles has many options and equations to use depending on what is given
Cosine A = b²+c²-a²
2(b)(c)
If given Angle A and side A
Cosine B = a²+c²-b²
Can be used as this to solve for a missing angle. Simply divide the two sides and take the cosine-¹ of the answer
When you have 2 Sides and Angle A,B, or C you can find out Side a,b or c
This works for Sine, Cosine and Tangent as long as the equation is rewritten correctly
2(a)(c)
You can find out another angle or side as long as you have one of them. Using whats call Sine Law
Cosine C = a²+b²-c²
Angle A X
2(a)(b)
=
Side A Side B
a²=b²+c²-2(b)(c)(Cosine A)
b²=a²+c²-2(a)(c)(Cosine B)
c²=a²+b²-2(a)(b)(Cosine C)
Side A X
=
Angle A Angle B