Question

I need help finding if it’s either SOH, CAH or TOA and the indicated side of the triangle, thank you!

Answer 1

`\huge\boxed{IJ \approx 2.01}`

Explanation:

In order to find the side mentioned (IJ), we need to use SOH CAH TOA.

SOH CAH TOA is an acronym to help us remember what sin, cos, and tan mean. It stands for:

Sin = Opposite / Hypotenuse

Cosine = Adjacent / Hypotenuse

Tan = Opposite / Adjacent

Since we know the measure of angle K (42) and we know one of the sides, we can use this to find the missing length.

Since the side given to us is the hypotenuse, and we're looking for the side opposite of the angle (IJ), the only possible one to use would be SIN as it includes Opposite and Hypotenuse.

Our equation is now this:
`\text{sin(42)} = (x)/(3)`

Let's now solve for x.

• 
  `\text{sin(42)} = (x)/(3)`
• 
  `3 \cdot \text{sin(42)} = x`
• 
  `\text{sin(42)} \approx 0.67`
• 
  `3 \cdot 0.67 \approx 2.01`

Therefore, the length of IJ will be around 2.01.

Hope this helped!