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A little confused with how to use SOHCAHTOA

Hi. Ok, so I know what SOHCAHTOA stands for, and which one you'd use if there was a missing side and angle. For example, you knew the hypotenuse and the adjacent, but you didn't know the opposite, you'd use cos^-1 to find the missing angle.

However, I don't understand it when you need to work out the length of a side, but know the angle. There's a question that tells you the length of the opposite and the angle, but the hypotenuse value and adjacent value are missing. How do I know which function to use? Please help, thanks.


Posted from TSR Mobile
It depends on whether you are trying to find the hypotenuse or the adjacent. The question will tell you which one you need.
You can work out one of the missing values using SOHCAHTOA, then use Pythagoras theorem to work out the final side (unless you wanna use SOHCAHTOA for both, which is fine). In your case:

Sin(x) = y / H where x is the given angle and y is the length of the opposite.

Re-arrange to get H = y / sin (x) which gives you the hypotenuse length. Repeat for the final length or use Pythagoras.
If the opposite is given, the question will then ask you to find one of the lengths, which will be the hypotenuse or the adjacent.

Eg

ABC = 90 degrees
AB = 6

ACB = 76 degrees.

Find length BC. (adjacent)

So you'd use

Tan76 = 6/BC
BC = 6/Tan76

Original post by Mr M
It depends on whether you are trying to find the hypotenuse or the adjacent. The question will tell you which one you need.


Ok, so if I needed to find the opposite, I'd use cos?


Posted from TSR Mobile
Reply 5
Avatar for joostan
joostan
13
Original post by Enthusiastic A
Ok, so if I needed to find the opposite, I'd use cos?


Posted from TSR Mobile


Cos is adjacent/hypotenuse , you'd need sin for that :smile:
Original post by Enthusiastic A
Ok, so if I needed to find the opposite, I'd use cos?


Posted from TSR Mobile


You never use cos for the opposite. cos x is defined as adjacent over hypotenuse.
Original post by joostan
Cos is adjacent/hypotenuse , you'd need sin for that :smile:


That's where I'm confused. I don't know the opposite, so how can I use sin (opposite/hypotenuse)? How can I divide the opposite by the hypotenuse when I don't know the value of the oposite?


Posted from TSR Mobile
(edited 11 years ago)
Original post by Enthusiastic A
That's where I'm confused. I don't know the opposite, so how can I use sin (opposite/hypotenuse)? How can I divide the opposite by the hypotenuse when I don't know the value of the oposite?


Posted from TSR Mobile


Call the unknown x?
Original post by Enthusiastic A
That's where I'm confused. I don't know the opposite, so how can I use sin (opposite/hypotenuse)? How can I divide the opposite by the hypotenuse when I don't know the value of the oposite?


Posted from TSR Mobile


How would you solve:

2 = x/4

Same thing. Different values.
Reply 10
Avatar for joostan
joostan
13
Original post by Enthusiastic A
That's where I'm confused. I don't know the opposite, so how can I use sin (opposite/hypotenuse)? How can I divide the opposite by the hypotenuse when I don't know the value of the oposite?


Posted from TSR Mobile


Rotate your page so that the angle you are looking at changes, then you can find that angle using trigonometry. Also as angles in a triangle sum to 180 you can find the required angle.

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