A man observes that the angle of elevation on the top of a tree is 24°,he walks 43 m towards the tree and observes that the angle of elevation is 37°,find the height of the tree?
3 answers
I don't know it
angles in left triangle are 24 + (180-37) + A = 180
where A is up top
so 24 +A -37 = 0
A = 13 degrees
then law of sines in that triangle
sin 24 / z = sin 13 / 43 where z is the hypotenuse up in the little triangle
.407 / z = .225/43
z = 77.8
now the right triangle on the right by the pole
we know the hypotenuse is 77.8
we know the angle opposit the pole is 37 deg
so
sin 37 = h/77.8
h = 46.8 meters height
where A is up top
so 24 +A -37 = 0
A = 13 degrees
then law of sines in that triangle
sin 24 / z = sin 13 / 43 where z is the hypotenuse up in the little triangle
.407 / z = .225/43
z = 77.8
now the right triangle on the right by the pole
we know the hypotenuse is 77.8
we know the angle opposit the pole is 37 deg
so
sin 37 = h/77.8
h = 46.8 meters height
Make a sketch, label the origianal position A and the new position B so that
AB = 43
Label the top of the tree as P and its bottom Q
In triangle ABP you have angle A = 24°, angle ABP = 143°, so angle APB = 13°
by the sine law:
BP/sin24 = 43/sin13, BP = 77.75
In the right-angled triangle, sin37° = h/BP
h = BPsin37 = 46.79
Another type of solution is to use the cotangent, often used for this style
of question by oobleck, and results in
height = 43/(cot24 - cot37) to obtain the same result.
AB = 43
Label the top of the tree as P and its bottom Q
In triangle ABP you have angle A = 24°, angle ABP = 143°, so angle APB = 13°
by the sine law:
BP/sin24 = 43/sin13, BP = 77.75
In the right-angled triangle, sin37° = h/BP
h = BPsin37 = 46.79
Another type of solution is to use the cotangent, often used for this style
of question by oobleck, and results in
height = 43/(cot24 - cot37) to obtain the same result.
2 answers