Find the missing length (trig)

In summary, The conversation discusses using the tangent function to find missing lengths in a right triangle. The notation "x tan" and "h tan" refer to the opposite and adjacent sides, respectively. The conversation also includes an example of using the tangent function to find the height of a ladder leaning against a wall. Overall, the conversation emphasizes the importance of understanding and correctly using the tangent function.
  • #1
uperkurk
167
0
Am I doing this correctly.

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[tex]x \tan=\frac{183}{\tan 30}=317ft[/tex]

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

[tex]h \tan=\frac{x}{\tan 60}=hft[/tex]
 
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  • #2
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
$$x = \frac{h}{\tan(30)}$$
 
  • #3
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:

[tex]x \tan=\frac{6.25}{\tan 15.5}=23ft[/tex]
 
  • #4
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.
 
  • #5
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!
 
  • #6
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"?
 
  • #7
Nope, the side is just labled as [tex]x[/tex] and then it just says

[tex]x\tan= ...[/tex]
 

What is the Pythagorean theorem and how is it used to find the missing length?

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be represented as c² = a² + b², where c is the length of the hypotenuse and a and b are the lengths of the other two sides. This theorem can be used to find the missing length in a right triangle by rearranging the equation to solve for the missing side length.

What is the sine ratio and how is it used to find the missing length?

The sine ratio is a trigonometric function that relates the side lengths of a right triangle to its angles. It is defined as the ratio of the length of the side opposite the given angle to the length of the hypotenuse. This can be represented as sin(theta) = opposite/hypotenuse. To find the missing length in a right triangle using the sine ratio, you would use the inverse sine function (sin^-1) to solve for the missing side length.

What is the cosine ratio and how is it used to find the missing length?

The cosine ratio is another trigonometric function that relates the side lengths of a right triangle to its angles. It is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. This can be represented as cos(theta) = adjacent/hypotenuse. To find the missing length in a right triangle using the cosine ratio, you would use the inverse cosine function (cos^-1) to solve for the missing side length.

What is the tangent ratio and how is it used to find the missing length?

The tangent ratio is another trigonometric function that relates the side lengths of a right triangle to its angles. It is defined as the ratio of the length of the side opposite the given angle to the length of the adjacent side. This can be represented as tan(theta) = opposite/adjacent. To find the missing length in a right triangle using the tangent ratio, you would use the inverse tangent function (tan^-1) to solve for the missing side length.

What are the common mistakes to avoid when using trigonometric ratios to find the missing length?

Some common mistakes to avoid when using trigonometric ratios to find the missing length include using the wrong ratio for the given angle, using the wrong units (degrees instead of radians or vice versa), forgetting to apply the inverse function to solve for the missing length, and rounding too early in the calculation process. It is important to double check your calculations and units to ensure an accurate answer.

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