SOLUTION: Caitlin wants to calculate the height of a tree on the opposite bank of a river. To do this, she lays out a baseline of 100 m long and measures the angles along the baseline to be

Algebra ->  Rational-functions -> SOLUTION: Caitlin wants to calculate the height of a tree on the opposite bank of a river. To do this, she lays out a baseline of 100 m long and measures the angles along the baseline to be      Log On


   

Question 1139856: Caitlin wants to calculate the height of a tree on the opposite bank of a river. To do this, she lays out a baseline of 100 m long and measures the angles along the baseline to be 80° and 27°. From the corner with the 80° angle, the angle of elevation to the top of the tree is 26°. Is this information sufficient to solve the problem? If so, determine the height, h, of the tree to the nearest tenth of a metre. If not, explain what would be needed to solve the problem.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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calculate the height of a tree on the opposite bank of a river.
To do this, she lays out a baseline of 100 m long and measures the angles along the baseline to be 80° and 27°.
From the corner with the 80° angle, the angle of elevation to the top of the tree is 26°.
:
A triangle ABC is formed
A = 80 degrees
B = 27 degrees
C: 180-80-27 = 73 degrees, the angle at the base of the tree
Find the distance from A to C, which we call b, distance from the tree to A
Use the law of sines
b%2Fsin%2827%29 = 100%2Fsin%2873%29
cross multiply
sin(73)b = sin(27)*100
b = 95.63%2Fsin%2827%29
b = 210.64 m from A to the base of the tree
then a right triangle is formed from A to the top of the tree elevation angle is 26 degrees
Height of the tree = h
tan(26) = h%2F210.64
h = 210.64 * tan(26)
h = 102.74 meters is the height of the tree