Im not sure how to do this...

B

boblee

New member
Joined
Jun 14, 2024
Messages
1
1718343976130.pngPlease just send a diagram with steps on how you did it... I am sure I already know how but for some reason I keep getting wrong answer
 
boblee said:
I keep getting wrong answer
Click to expand...
Hi boblee. When I tried to find the measure of angle BST first, I got a Complex number with an Imaginary part. Either I've goofed up something or there's a misprint in the exercise statement. Here's my diagram (not to scale).

724FAD9E-9207-41CF-9100-D13808260247.jpeg

We're told that the distance from the sailboat to Brit (SB) is the same as to Tara (ST). When I used tangent to find that distance, I got a number that's less than half the distance BT. In other words, the triangle BST does not exist. (That's why the law of cosines gave me a Complex number for the angle at S.)

If the angle of elevation were smaller, then I would get a sensible answer. For example, if I change 51° to 41°, then my final answer (angle TBS, rounded) is 42.8°.

What did you try? :)
 
Otis said:
If the angle of elevation were smaller, then I would get a sensible answer. For example, if I change 51° to 41°, then my final answer (angle TBS, rounded) is 42.8°.
Click to expand...
I agree. The angle of elevation has to be less than 49.844 degrees to work. I'm wondering it they gave the complement of the angle they intended, and it should be 39 rather than 51.

Of course, the problem doesn't mention how far the dock is above the water (and the presumed base of the mast?), and how tall the girls are, both of which affect the effective height and the angle of elevation as seen from their eyes.
 
Dr.Peterson said:
the problem doesn't mention how far the dock is above the water (and the presumed base of the mast?), and how tall the girls are
Click to expand...
I almost mentioned that eyeballs need to be at sea level (that is, place S,B,T on the same plane), but I passed on that. This seems like one of those "stylized" word problems where we're supposed to ignore such pesky details of reality, heh. 🙃

Thanks for posting the confirmation.

PS: I also think they ought to have said "equidistant from each girl" instead of "equidistant between both girls".
 
Beer induced reaction follows.
boblee said:
View attachment 38170Please just send a diagram with steps on how you did it... I am sure I already know how but for some reason I keep getting wrong answer
Click to expand...
1718343976130.png
Otis said:
Hi boblee. When I tried to find the measure of angle BST first, I got a Complex number with an Imaginary part. Either I've goofed up something or there's a misprint in the exercise statement. Here's my diagram (not to scale).

View attachment 38174

We're told that the distance from the sailboat to Brit (SB) is the same as to Tara (ST). When I used tangent to find that distance, I got a number that's less than half the distance BT. In other words, the triangle BST does not exist. (That's why the law of cosines gave me a Complex number for the angle at S.)

If the angle of elevation were smaller, then I would get a sensible answer. For example, if I change 51° to 41°, then my final answer (angle TBS, rounded) is 42.8°.

What did you try? :)
Click to expand...

Brit and Tara are standing 13.5 m apart on a dock when they observe a sailboat moving parallel to the dock. ...

Highlighting the first sentence to do a web search,


solving triangles

Brit and Tara are standing 8.8 m apart on a dock when they observe a sailboat moving parallel to the dock. When the boat is equidistant between both girls, the angle of elevation to the top of its 8.0 m mast is 51 degrees for both observers. Describe how you would calculate the angle, to the...
mathforums.com

A notable AI attempt from this web search gives the following dubious result:
 
jonah2.0 said:
Beer induced reaction
Click to expand...
Thanks for posting, Sir Jonah. Your linked Math Forums page shows that a correct version of this exercise may be solved by students who've learned only right-triangle definitions for sine, cosine and tangent. Using the law of cosines (one of my favorites) is valid, but not required. :)
 
Beer induced reaction follows.
Otis said:
Thanks for posting, Sir Jonah. Your linked Math Forums page shows that a correct version of this exercise may be solved by students who've learned only right-triangle definitions for sine, cosine and tangent. Using the law of cosines (one of my favorites) is valid, but not required. :)
Click to expand...
It was the quizlet.com link that first gave me the heads up about the 13.5 m. typo.
I can't remember ever seeing that Math Forums page until yesterday's web search; maybe I did see it 9 years ago but my memory of ever seeing it is simply gone from either old age or booze indulgence. I wish I could also easily forget them unpleasant memories.
Screenshot_20240616-054954_Chrome.jpg

Had to resort to the standard lazy hack of web search as I was feeling somewhat dumb and rusty yesterday. My imagination must still be in need of some brandy lubrication as I can't seem to visualize what you meant by "but not required". Is there a right-triangle definition for sine, cosine and tangent as it applies to this problem that I'm missing that doesn't require use of the law of cosines?
 
Last edited:
Comment 1: I don't see how 13.5 can be a typo. There just seem to be several sources that use that number, and others that use 8.8; both come from books, but the former version is bad. How they both came to exist is a mystery. (There's no reason the distance "must" be 8.8 m!)

1718498500434.png

1718498532487.png

Comment 2: I didn't use the law of cosines when I solved it; they ask for angle ABT, so we break the isosceles triangle ABT into two right triangles and find that cos(ABT) = 4.4/AB = 0.68, and angle ABT = 47.15 degrees (for this version, with BT = 8.8).
 
Beer induced reaction follows.
Dr.Peterson said:
Comment 2: I didn't use the law of cosines when I solved it; they ask for angle ABT, so we break the isosceles triangle ABT into two right triangles and find that cos(ABT) = 4.4/AB = 0.68, and angle ABT = 47.15 degrees (for this version, with BT = 8.8).
Click to expand...
I really should have seen that one a mile away. Induced tunnel vision from seeing how it was done in the web search links.
 
You must log in or register to reply here.
Top