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Period 3

SoHCahToa Project

Cosine (Cah)

Cosine Function: Cos(angle) = Adjacent / Hypotenuse

In a right triangle the cosine of an angle is the length of the adjacent side divided by the length of the hypotenuse.

cos 60* = adjacent / hypotenuse = h / 1000

cos 60* = 0.5

Sine (Soh)

0.5 = h / 1000

1000 m

60*

h

swap sides: h / 1000 = 0.5

Multiply both

sides by 1000: h = 0.5 x 1000 =500 m

The height of h= 500 m

Sine Function: Sin(angle) = Opposite / Hypotenuse

In any right triangle, the sine of an angle x is the length of the opposite side divided by the length of the hypotenuse.

Hypotenuse

68*

Start with: sin 68* = 70/w

multiply both

sides by w: w x (sin 68*) = 70

Divide both

sides by "sin 68*: w = 70/ (sin 68)

Calculate: w = 70 / 0.9271 = 75.5m

The length of W = 75.5

Adjacent side

W

70m

Tangent (Toa)

Opposite

side

Tangent Function: Tan(angle) = Opposite / Adjacent

In a right triangle, the tangent of an angle is the length of the opposite side divided by the length of the adjacent side.

start with: tan 53* = a/7

Swap: a/7 = tan 53*

Calculate tan 53*: a/7 = 1.327

Multiply both sides by 7:

a = 1.327 x 7 = 9.29

a

side "a" = 9.29

53*

7

Pythagorean Theorem

The formula for Pythagorean Theorem: a2+b2=c2

"c" is the longest side of the triangle and "a" and "b" are the other two sides. If we know the lengths of two sides of a right angled triangle, we can find the length of the third side.

a2 + b2 = c2

5(5) + 12(12) = c2

25 + 144 = c2

169 = c2

c2 = 169

c = square root 169

c = 13

5

c

a

12

b

Theta

Variable to represent an angle of unknown degrees.

0

4

6

Opposite

"Opposite" is opposite to the angle. No matter where the angle is on the right triangle is will always be opposite from it.

0

Opposite

Adjacent

"Adjacent" is always adjacent or next to the angle.

0

Adjacent

Leg

In a right triangle, a leg is either of the two sides that form the right angle. Not the Hypotenuse.

leg

Hypotenuse

The side of a right triangle opposite the right angle. The hypotenuse is the longest side of the right triangle

Hypotenuse

6

4

3

Jason Mallare

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