Find the missing length (trig)

  • Thread starter Thread starter uperkurk
  • Start date Start date
  • Tags Tags
    Length Trig
AI Thread Summary
The discussion revolves around using trigonometric functions to find missing lengths in right triangles. The user is trying to confirm their calculations involving tangent ratios, specifically for a triangle with a height of 183 ft and an unknown base length. They also pose a question about a ladder's height against a wall, confirming their calculations using the tangent of the angles involved. The notation "x tan" is clarified as a specific format from their learning material, not standard notation. The conversation emphasizes the importance of understanding trigonometric relationships in solving geometric problems.
uperkurk
Messages
167
Reaction score
0
Am I doing this correctly.

VEa0He3.png


x \tan=\frac{183}{\tan 30}=317ft

Also if it were the other way around and I needed to find the height but I already had the length would it just be

h \tan=\frac{x}{\tan 60}=hft
 
Physics news on Phys.org
I'm not sure what the notation ##x \tan## and ##h \tan## means.

If ##h## refers to the height of the triangle (currently labeled 183 ft), then both of the following are true:
$$\tan(60) = \frac{x}{h}$$
and
$$\tan(30) = \frac{h}{x}$$
So if you know ##x## but not ##h##, then you can find ##h## by either
$$h = \frac{x}{\tan(60)}$$
or
$$h = x\tan(30)$$
And if you know ##h## but not ##x##, then you can find ##x## by either
$$x = h \tan(60)$$
or
$$x = \frac{h}{\tan(30)}$$
 
Thanks. I have 1 more question if you wouldn't mind confirming my answer. Just so I don't make another thread.

A ladder is leaning against a wall. The foot of the ladder is 6.25 feet from the wall.
The ladder makes an angle of 74.5° with the level ground. How high on the wall does the ladder
reach? Round the answer to the nearest tenth of a foot.

After working out the remaining angle being 15.5° I then have:

x \tan=\frac{6.25}{\tan 15.5}=23ft
 
Yes, it's correct, except again I'm not sure why you wrote "##x \tan##" instead of just ##x##.

By the way, homework and homework-like questions should go in the homework forums.
 
x tan is just the notation they use in this book I'm learning from. It's not really a homework question I'm an independant learner and this book doesn't have the answers in the back so just wanted someone to check I was doing these correctly.

Thanks!
 
Are you sure they are not writing something like "x tan(60)" where "x" is the length of the "opposite side" to get the "near side"?
 
Nope, the side is just labled as x and then it just says

x\tan= ...
 
Back
Top