Finding An Angle Using Law of Sines

[lilac_jade910]

Problem: An 8 meter pole is leaning against a tree. The foot of the pole is 5 meters from the foot of the tree. What angle does the pole make with the tree?

Answer: I am clueless when it comes to finding angles.

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I figured out that the height of the tree is 39 meters by using the pythagorean theorem (5^2*b^2=8^2), but I realise now that I didn't need to do that to solve the problem.

I am 100% clueless when it comes to finding angles using the Law of Sines, and I am hoping that someone would be able to help me with this.

 

[stapel]

I am clueless when it comes to finding angles.

So you haven't studied trigonometry yet? (This is a fairly simple "punch the inverse-sine button on your calculator" exercise, is why I ask.)

Thank you.

Eliz.

P.S. Welcome to FreeMathHelp!

 

[jonboy]

Howdy lilac_jade910!

I am 100% clueless when it comes to finding angles using the Law of Sines

This website looks nice - Law of Sines. Check it out and if you have any q's ask us. You don't need it for this problem though.

I figured out that the height of the tree is 39 meters by using the Pythagorean theorem (5^2*b^2=8^2), but I realize now that I didn't need to do that to solve the problem.

Pythagorean Theorem is a^2 + b^2 = c^2 not a^2 * b^2 = c^2

When your ready here's the answer -

Your sketch should resemble this:

Like Stapel/Eliz says, this is a "punch the inverse-sine button on your calculator" problem.

...Let \(\displaystyle X\) be the unknown angle: \(\displaystyle Sin\,X\,\,=\,\frac{5}{8}\)

New press Inverse Sine with this fraction in your calc.

...You get:\(\displaystyle \L \;m\,<\,X\,\approx\,38.7^o\)

 

[lilac_jade910]

Ack! Well, I /did/ add, not muliply... Anyway, thank you all for your help! It's greatly appreciated!

Eliz, yes and no I'm in part two of geometry, but I have a hard time understanding the trigonmetric ratios and all.

Thank you again!