use a cosine table. use Pythagorus to find the hypotenuse then you can use the cosine table to look it up the corresponding angle( cos x = 5 / 5.833, so x is approx. 31°
I have never heard of SOH-CAH-TOA. But the way I have always remembered it is a little jingle. Some Old Hen S=O/H Caught Another Hen C=A/H Taking Oscar Away T=O/A
Back in military, we were taught it as: Sally can’t tell, Oscar has a heap of apples. Written like this: Oscar Sally Has A Can’t Heap Of Tell Apples Later, I heard that it was taught in college as: Sally can’t tell, Oscar has a hit of acid.
Label the 3 vertices of the triangle with upper-case letters ABC Label the 3 sides of the triangle with lower-case letters abc ∠A = x° ---> opposite side a = 3 ∠B = 90° --> opposite side b = ? ∠C = y° --> opposite side c = 5 Using the Law of Sines : sinA/a = SinB/b = sinC/c Sin90°/b = SinA/3 --> won't work Have to use Pythagorean theorem to get side b b² = a² + c² b² = 3² + 5² b² = 9 + 25 = 34 b = √34 ≈ 5.83 Sin90°/5.83 = SinA/3 3·Sin90° = 5.83 · SinA SinA = 3·Sin90 / 5.83 SinA = 3 · 1 / 5.83 SinA = sin-1(0.51457) ≈ 30.96° ∠A ≈ 30.96°✅ ----------------------------------------------------------------------- Using : SOHCAHTOA SinA = opposite/hypotenuse = a/b = 3/? CosA = adjacent/hypotenuse = c/b = 5/? TanA = opposite/adjacent = a/c = 3/5 TanA = tan-1(3/5) = 30.96° ∠A ≈ 30.96°✅
Is geometry really necessary if you're not going to be either or architect or Carpenter personally I don't think it is.. that's why I was never motivated to learn it I have no desire to be either one
use angles of special angles of triangles that you have memorized and interpolation. You won't get an as accurate an answer but depending on the context it might be good enough. For example using interpolation with the given measures and the memorized fact that tan 30° = .577 I get x is approx. 31.2. So to the nearest whole degree x = approximately 31°
I finally discovered the ‘2nd’ button on my iPhone15 Scientific Calculator flipped the trig function buttons in to inverse/arc modes just prior to the end of this video explaining the same…. 🙄
Do you know that trigonometry was invented by Hindus in India. They used it to help in navigation. The word trigonometry is a mutation of Sanskrit word for this subject which is Tricone-metra. It means triangle measurement.
x = 30.96°. Thank you
thanks for the calculator lesson
So how would you do this without a calculator?
use a cosine table. use Pythagorus to find the hypotenuse then you can use the cosine table to look it up the corresponding angle( cos x = 5 / 5.833, so x is approx. 31°
I have never heard of
SOH-CAH-TOA.
But the way I have always remembered it is a little jingle.
Some Old Hen
S=O/H
Caught Another Hen
C=A/H
Taking Oscar Away
T=O/A
@totalcardetailing2022. I was taught 40 years ago in the UK the following saying instead: Some officers have Curly auburn hair till old age.
Nice acronym ❤❤❤
With us I knew it as OSHACHOTA
S= O/H
C=A/H
T=O/A
Back in military, we were taught it as: Sally can’t tell, Oscar has a heap of apples. Written like this:
Oscar
Sally Has
A
Can’t Heap
Of
Tell Apples
Later, I heard that it was taught in college as: Sally can’t tell, Oscar has a hit of acid.
Answer:
x = 30.96 degrees
------------
Opposite
Tan x = -----
Adjacent
3
Tan x = --- = 0.6
5
Tan-1 (0.6)=
30.96 degrees
Looked like a 30/60/90 right triangle to me, hwich wasn't too far off the mark :D
Easy to see that tangent is also sine/cosine.
tan(x)=3/5
=0.6
arctan(0.6) = 30.964°
tan x = 3/5 so x = tan-¹ 3/5 ~ 30.96° and the other corners 90° and 90 - 30.96 = 59.04°
x° = arcTan(3/5) = arcSin(3√34) = arcCos(5/√34)
∅⁰=Arctan(3/5)
Had to find my cosine table that I have had since 1974. Yes, a paper booklet.
Label the 3 vertices of the triangle with upper-case letters ABC
Label the 3 sides of the triangle with lower-case letters abc
∠A = x° ---> opposite side a = 3
∠B = 90° --> opposite side b = ?
∠C = y° --> opposite side c = 5
Using the Law of Sines :
sinA/a = SinB/b = sinC/c
Sin90°/b = SinA/3 --> won't work
Have to use Pythagorean theorem to get side b
b² = a² + c²
b² = 3² + 5²
b² = 9 + 25 = 34
b = √34 ≈ 5.83
Sin90°/5.83 = SinA/3
3·Sin90° = 5.83 · SinA
SinA = 3·Sin90 / 5.83
SinA = 3 · 1 / 5.83
SinA = sin-1(0.51457) ≈ 30.96°
∠A ≈ 30.96°✅
-----------------------------------------------------------------------
Using : SOHCAHTOA
SinA = opposite/hypotenuse = a/b = 3/?
CosA = adjacent/hypotenuse = c/b = 5/?
TanA = opposite/adjacent = a/c = 3/5
TanA = tan-1(3/5) = 30.96°
∠A ≈ 30.96°✅
90 ÷8×3
Is geometry really necessary if you're not going to be either or architect or Carpenter personally I don't think it is.. that's why I was never motivated to learn it I have no desire to be either one
Yes. Geometry is necessary. Furthermore, all math is really geometry. Most math, anyway.
Right angle trigonometry?!
All trigonometry is specific to triangles with a right [90°] angle!
...so whats the math without the calculator?
use angles of special angles of triangles that you have memorized and interpolation. You won't get an as accurate an answer but depending on the context it might be good enough. For example using interpolation with the given measures and the memorized fact that tan 30° = .577 I get x is approx. 31.2. So to the nearest whole degree x = approximately 31°
I finally discovered the ‘2nd’ button on my iPhone15 Scientific Calculator flipped the trig function buttons in to inverse/arc modes just prior to the end of this video explaining the same…. 🙄
Do you know that trigonometry was invented by Hindus in India. They used it to help in navigation. The word trigonometry is a mutation of Sanskrit word for this subject which is Tricone-metra. It means triangle measurement.
Ok...
60?
へーー 海外では このような覚え方するんですね SOH -CAH-TOA 面白いです。
30.96375653207 Degrees
OR
30° 57' 49.52"