SOLUTION: The figure below is a diagram that shows how Colleen estimates the height of a tree that is on the other side of a stream. She stands at point A facing the tree and finds the angle

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Question 1169496: The figure below is a diagram that shows how Colleen estimates the height of a tree that is on the other side of a stream. She stands at point A facing the tree and finds the angle of elevation from A to the top of the tree to be 59°. Then she turns 110° and walks 25 feet to point B, where she measures the angle between her path AB and the line BC extending from her to the base of the tree. She finds that angle to be 36°. Use this information to find the height of the tree. (Round your answer to the nearest whole number.)
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The figure below is a diagram that shows how Colleen estimates the height of a tree that is on the other side of a stream.
She stands at point A facing the tree and finds the angle of elevation from A to the top of the tree to be 59°.
Then she turns 110° and walks 25 feet to point B, where she measures the angle between her path AB and the line BC extending from her to the base of the tree.
She finds that angle to be 36°. Use this information to find the height of the tree. (Round your answer to the nearest whole number.)
:
Find the distance from the observer to the base of the tree. Triangle ABC
Where A = 110 degrees, B = 36 degrees and c = 25 ft
Find C: 180 - 110 - 36 = 34 degrees
Use the law of sines to find b, the distance from A to C (the base of the tree)
=
Cross multiply
sin(34)b = sin(36)*25
b =
b = 26.278 ft from A to the base of the tree.
:
Find the height of the tree.
A right triangle is formed, ACT(top of the tree)
Let h = the height of the tree
Use the tangent of 59 degrees
tan(59) =
h = tan(59) * 26.278
h = 43.73 ~ 44 ft is the height of the tree.