Trig again

[halfdeadzombie]

This is harder than the extra credit was, how wrong is that?


When the sun's angle of elivation is 76 degrees, a tree tilted at an angle of 4 degrees from the vertical casts a 18-foot shadow on the ground. Find the length of the tree to the nearest tenth.

So do I just subtract 4 from 76 and then do 72sin * 18? That would give me 17.1 wich isnt one of the choises. (thank the lord for multiple choice questions)

 

[Gene]

Nope, that only works for right triangles. The problem is lousy 'cause they don't say if the tree is leaning toward the sun, away from it or indeed in any other direction.
You seem to favor away from the sun. That gives a triangle with A the top of the tree, B the foot and C the end of the shadow.
You subtract 4° from 90° for angle B = 86°.
Angle C = 76°
Side c is the tree
That makes angle A = 18°
Side a = 18'
If you know the Law of Sines, use that.
sin(A)/a = sin(C)/c

 

[halfdeadzombie]

So you would set up a proportion,

0.30 X
---- = -----
18 0.97

right?

 

[Gene]

Huh :?:
sin(A)/a = sin(C)/c
sin(18)/18 = sin(76)/X
You flipped :!:

 

[halfdeadzombie]

so the answer would be 56.5. I see now.

 

[halfdeadzombie]

but how did you figure angle a to be 18?

 

[Gene]

The sum of the three angles of a triangle = 180°.
76+86+A=180