HELP PLEASE! I need to find the height h of the tree. It is leaning 1° from the vertical At a point d = 39 meters from the tree...?
Because of prevailing winds, a tree grew so that it was leaning 1° from the vertical. At a point d = 39 meters from the tree, the angle of elevation to the top of the trees is a = 32°. Find the height h of the tree. (Round your answer to one decimal place.)
THIS IS WHAT I DID AND GOT IT WRONG.... HELP PLEASE PLEASE PLEASE
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You had the right idea, using the law of sines, but one of your angles was off. The angle opposite the 39 m side is 180 - 32 - 91 = 57° (the 91 comes from the fact that the tree is bent 1° away from making it a right triangle). now plug this in and you should get the right answer:
39 / sin(57) = h / sin(32)
h = [39 / sin(57)] · sin(32) ≈ 24.6 m
EDIT: I made the assumption that the tree is leaning directly away from you, but as the other answers point out, the problem isn't specific about this point. So a satisfactory answer would be "not enough information".
The angle at point B is either 89º or 91º; the problem didn't say which way the tree was leaning (away from you would make <B = 91º, for example).
That makes the third angle either be 57 or 59 degrees and that's what would go under the 39 in your sine law equation.
assume the 1 degree is towards the observer.
h = height
x = distance from base of tree to vertical height line
h/sin89 = x/sin1
h/(39-x) = tan 32
h = 57.29x = (39-x)tan 32 = 24.37-0.625x
57.915x = 24.37
x = 0.42
h = 24.1 m
you didn't account for the 1 degree from vertical.
angle b is 89 degrees. angle a is 32 degrees
the longest side is along the ground or 39 m
drop an altitude from point c (which you didn't label) to ab
that altitude is the same for 2 right triangles
a=x*sin(32)=(39-x)*sin(89)
xsin(32)=39sin(89)-xsin(89)
xsin(32)+xsin(89)=39sin(89)
x(sin(32)+sin(89))=39sin(89)
x=39sin(89)/(sin(32)+sin(89)
evaluate x then find a
of course why I didn't use the law of sines... derp
The three angles are 32, 89 and 59 ..... ( 180 - 89 - 32 )
Let x be the height of the tree ( opposite to 32 d )
Using the Law of Sines
...... x .......---.. 39
.....---------- = ------------
..... sin 32 .... sin 59
The x = 39 sin 32 / sin 59 = 24.11 meters ............ THE END
The tree could be leaning one degree in ANY direction. If it's leaning to the side, relative to you, your answer is correct.
ab=39*tg32º
ab=39*0.62
ab=24.36 m
148° ??? a + b + c = 180 ---> c = 180 - 32 - 89...tsk