What is 2nd Sine? Solving a Triangle with 13.5 Hypotenuse

[Liam C]

Homework Statement

A triangle with a hypotenuse of 13.5 and height of 11.8. Find the measure of angle P.
Angle p is on the same line as the 90 degree angle and I found out that it must be sine.

Homework Equations

sine = opposite/hypotenuse

The Attempt at a Solution

sin p = 11.8/13.5
sin p = .874

Textbooks answer: sin p = 71.468
It says I need to use something called 2nd sine like this: 2nd sin(11.8/13.5), which I can't find on my calculator and hasn't been introduced in the textbook until now. It doesn't explain 2nd sin. What does it mean and how do I go about solving this on my own?

 

[Charles Link]

It would appear "2nd" is supposed to be an inverse function: You're finding the angle whose sine is 11.8/13.5. That is often written as $\sin^{-1}(11.8/13.5)$. The "2nd" is apparently referring to a "second" (inverse) function.

 

[berkeman]

Textbooks answer: sin p = 71.468

That looks more like the angle p. Try looking for arcsin on your calculator to go from the sine value to the angle...

EDIT -- Beaten to the punch by Charles

 

[berkeman]

Textbooks answer: sin p = 71.468

BTW, I get a slightly different answer for the angle. I'll check the rest of your work (unless Charles beats me to that too!).

 

[berkeman]

Angle p is on the same line as the 90 degree angle and I found out that it must be sine.

Are you sure you have the angle p shown in the right place?

 

[Liam C]

Are you sure you have the angle p shown in the right place?

Yes.

 

[Liam C]

Are you sure you have the angle p shown in the right place?

Also I tried using the inverse sine and it didn't give me the correct answer. It gives me 60.9

 

[berkeman]

Yes.

So what do you get for arcsin(11.8/13.5 )

EDIT -- Right, that's what I got.

 

[Liam C]

So what do you get for arcsin(11.8/13.5 )

EDIT -- Right, that's what I got.

I don't know how to do that, unfortunately.

 

[berkeman]

I don't know how to do that, unfortunately.

arcsine is the same as inverse sine.

 

[berkeman]

arcsine is the same as inverse sine.

http://www.rapidtables.com/math/trigonometry/arcsin.htm

 

[Liam C]

http://www.rapidtables.com/math/trigonometry/arcsin.htm

Oh thank you for the link. I will read it.

 

[berkeman]

hypotenuse of 13.5 and height of 11.8.

Maybe double-check those numbers -- maybe there is a typo digit in there somewhere that is giving us the wrong answer...

 

[Liam C]

Maybe double-check those numbers -- maybe there is a typo digit in there somewhere that is giving us the wrong answer...

Unfortunately no :(
I am starting to think there might be a typo in the textbook given the fact what it's telling me to do gives me a completely wrong answer

 

[berkeman]

The Attempt at a Solution

sin p = 11.8/13.5
sin p = .874

Textbooks answer: sin p = 71.468

arcsin(12.8/13.5) = 71.468. That looks to be the typo.

 

[Liam C]

arcsin(12.8/13.5) = 71.468. That looks to be the typo.

Ah, thanks so much! A silly textbook typo had me so confused!

 

[Mark44]

It says I need to use something called 2nd sine like this: 2nd sin(11.8/13.5),

Some calculators have a button labeled "2nd". When you press it, the calculator uses the function behind (or above) a given button.

On my calculator, a CASIO model, there is a button labeled SHIFT, in orange letters. Just above my button labeled "sin" is label, in orange letters, for the inverse function "sin^-1". There are inverse functions for sine, cosine, and tangent, as well as log, ln (natural log) and a few others. All of the inverse functions are accessed by pressing the SHIFT button. On yours I'd be willing to bet there's a "2nd" button.

 

[Liam C]

Some calculators have a button labeled "2nd". When you press it, the calculator uses the function behind (or above) a given button.

On my calculator, a CASIO model, there is a button labeled SHIFT, in orange letters. Just above my button labeled "sin" is label, in orange letters, for the inverse function "sin^-1". There are inverse functions for sine, cosine, and tangent, as well as log, ln (natural log) and a few others. All of the inverse functions are accessed by pressing the SHIFT button. On yours I'd be willing to bet there's a "2nd" button.

Yes, shift did it :)