How to find sides in Right Triangles?

Question

I have been working with finding sides (given one side and an angle) in Right triangles and have improved greatly with determine the trig function to use.

My question is how do I determine if I multiply to get an answer, ex: 7tan(45) or divide, ex:4/sin(35)

What information is being provided that determine whether I multiply or divide to arrive at a final answer?

Thank you,

Brian

Answer 1

What determines whether you multiply or divide is what you are solving for. If you are solving for" x " then you have to isolate it by using the inverse operation.

Example 1: 2x= sin(30°)

We must isolate the variable x so we divide each side of the equation by 2. It is equivalent to say we are multiplying by 1/2 which is the reciprocal of 2. Then 2 divided by 2 gives us 1.

then we get (1/2) 2x= (1/2) sin(30°)

thus, x= (1/2) sin(30°) we know sin(30°) = 1/2

x= (1/2) (1/2)

x= 1/4

Example 2: y/3= sin(30^o)

We must isolate the variable x so we multiply each side of the equation by 3. It is equivalent to say we are dividing by 1/3 which is the reciprocal of 3. Then 1/3 multiplied by 3 gives us 1.

then we get (3)(y/3)= (3) sin(30°)

thus, y= (3) sin(30°) we know sin(30°) = 1/2

y= (3) (1/2)

y= 3/2

NOTE: There two examples are if you are looking for sides of a right triangle. Where X and Y are sides of the right triangle. If you need to look for the measure of an angle in a right triangle your equation might look like this example...

Example 3: 1/2 = sin(θ) where θ= the degree measure of an angle

In this case we must take the inverse of the function sine

1/2 = sin(θ) We can ask ourselves what angle measure of the sine function would give us 1/2 ?

sin^-1 (1/2)= θ

θ= 30°