Triangle Angles: Find b & c with A-B-C given

[logmode]

I am stuck on the job; I need to find the angles.
It’s not an angle or side based triangle, just a right triangle. The lengths are known, A-B-C. What I need to know is the angles, a-b-c. So, a=90*, what formula could I use to find b, and c? Sorry, please make it easy enough for me to work it out, I never made it past algebra and failed geometry.

 

[BloodyFrozen]

Well, you could use law of sines. Plug in your values and solve for the desired angles

$$\frac{sin(a)}{A} = \frac{sin(b)}{B} = \frac{sin(c)}{C} = 2R$$

However, this is past algebra and sometimes covered at the end of geometry.

 

[The1337gamer]

If this is a right angled triangle, could you not use trigonometry.
ie.

Cos(c) = adjacent/hypotenuse = B/A
Sin(c) = opposite/hypotenuse = C/A
Tan(c) = opposite/adjacent = C/B

Similarly for angle b

Cos(b) = C/A
Sin(b) = B/A
Tan(b) = B/C

 

[logmode]

That's over my head. Can you please break it down?

 

[The1337gamer]

Right, so you have a right angled triangle. The angle a = 90. The side opposite of angle a = A. The side opposite of angle b = B. The side opposite of angle c = C.

Now the longest side of a right angled triangle is known as the hypotenuse, this always happens to be the side opposite to the right angle, so side A = hypotenuse.

Now if we consider angle b, it is the angle between the side A (hypotenuse) and the side C. We call the side C the adjacent side. Then side B is the opposite (because it is the side opposite of angle b).

If we consider angle c, then A = hypotenuse, B = adjacent, C = opposite.

Now there are functions that relate the sides and angles of a triangle.

Cos (angle) = adjacent/hypotenuse
Sine (angle) = opposite/hypotenuse
Tan (angle) = opposite/adjacent

This is how you get the equations i wrote above. Now you can find the cos, sine, and tan function on a standard scientific calculator. So if you want to find the angle you do the inverse function of the ratio of the sides.

So depending what side you know, you can use either of the 3 equation

angle = inverse cos(adjacent/hypotenuse)
angle = inverse sine(opposite/hypotenuse)
angle = inverse tan(opposite/adjacent)

 

[BloodyFrozen]

By using the law of sines, we get

$$\frac{sin(a)}{A} = \frac{sin(b)}{B}$$

Since you know $a$, $A$, and $B$, you can solve for $b$.

$$\frac{B\cdot sin(a)}{A} = sin(b)$$
$$sin^{-1}(\frac{B\cdot sin(a)}{A}) = b$$

Likewise, you can also solve for $c$. Make sure your calculator setting is either on degrees or radians, depending on your situation.

 

[logmode]

Thank you very much for the helping hand. Trigonometry is awesome.

I understand now how to get the ratio. And I found how to use C, S, or T to change angle to a ratio (put in the angle and hit the C, S, or T key on the XP-W scientific calculator, to get the ratio of the sides.), but it was said: “so if you want to find the angle you do the inverse function of the ratio of the sides.”

If: HYP = 26.1725, ADJ = 26, and OPP = 3, a = 90* so,
COS (b) = C/A = .9934, or
SIN (b) = B/A = .1146, or
TAN (b) = B/C = .1154 …

How is the inverse function executed on my calculator?

 

[The1337gamer]

I'm not sure if it's different for each calculator, but the inverse function is denoted cos^(-1), sin^(-1), tan^(-1).

On my calculator it appears in yellow writing just above the sin, cos, and tan buttons.

So i have to press shift then sin to get inverse sin, shift cos to get inverse cos, shift tan to get inverse tan.

 

[The1337gamer]

Thank you very much for the helping hand. Trigonometry is awesome.

I understand now how to get the ratio. And I found how to use C, S, or T to change angle to a ratio (put in the angle and hit the C, S, or T key on the XP-W scientific calculator, to get the ratio of the sides.), but it was said: “so if you want to find the angle you do the inverse function of the ratio of the sides.”

If: HYP = 26.1725, ADJ = 26, and OPP = 3, a = 90* so,
COS (b) = C/A = .9934, or
SIN (b) = B/A = .1146, or
TAN (b) = C/B = 8.6666 …

How is the inverse function executed on my calculator?

Tan(b) = B/C = opp/adj

 

[logmode]

If: HYP = 26.1725, ADJ = 26, and OPP = 3, a = 90* so,
COS (b) = C/A = .9934, or
SIN (b) = B/A = .1146, or
TAN (b) = B/C = .1154 …
How is the inverse function executed on my calculator?
Answer: INV- button
So, COS ratio – INV button – COS button = angle = 6.58*pitch
Thank you very much

Finding the error is the hard part, fixing it is easy but rewarding. So let me reverse that, thank you gamer, you have a good eye.