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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

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