Question

Use of SOH CAH TOA
find the value of x and y

Answer 1

Explanation:

Sin, Cos, and Tangent are the three common trig functions.

Sine, when given an angle, is a right triangle ratio between the opp side of the angle /hypotenuse(the side opposite of the right triangle),

SOH

Cosine, when given an angle, is a right triangle ratio between the adj side of the angle/hypotenus(the side opposite of the right triangle)

CAH

Tangent, when given an angle, is a right triangle ratio between the opp side of the angle/ adj side of the angle

TOA.

So

given an angle, alpha,

`\sin( \alpha ) = (o)/(h)`

`\cos( \alpha ) = (a)/(h)`

`\tan( \alpha ) = (o)/(a)`

Problem 1, we know that the angle of reference is 53.1, the side adjacent to that angle is 30 cm, and we are trying to find x. and y.

Solving for x, the side length x is opposite of the angle 53.1

We have an angle, the adjacent side of the angle and the opposite side is what we are trying to find.

We use TAN

`\tan(53.1) = (x)/(30)`

We know

`\tan(53.1) = 1.33`

so

`1.33 = (x)/(30)`

`40 = x`

Now, since we know the side length of x, we have two ways to solve for y, which is the hypotenuse.

Remember the hypotenuse is the angle opposite of the 90° angle(right angle)

We could use Sine or Cosine

`\sin( 53.1) = (40)/(y)`

`0.8 = (40)/(y)`

`y = (40)/(0.8)`

`y= 50`

or

`\cos(53.1) = (30)/(y)`

`0.6 = (30)/(y)`

`y = 50`

So x=40, y=50

2. Do the same steps above

Solving for x,

`\sin(30) = (x)/(90)`

`45 = x`

Solving for y,

`\cos(30) = (y)/(90)`

cos(30)

`\cos(30) = ( √(3) )/(2)`

so

`( √(3) )/(2) = (y)/(90)`

`y = 45 √(3) = 77.942`