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45. Height of a tree. A tree is planted at a point O on horizo tal ground. Two points A and B on the ground are 100 feet apart. The angles of elevation of the top of the tree T from points A and B are 45° and 30°, respectively. The measure c LAOB is 60°. Find the height of the tree. T. 450 60° 30° A 100 feet

45. Height of a tree. A tree is planted at a point O on horizo tal ground. Two points A and B on the ground are 100 feet apart. The angles of elevation of the top of the tree T from points A and B are 45° and 30°, respectively. The measure c LAOB is 60°. Find the height of the tree. T. 450 60° 30° A 100 feet

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter6: Circles
Section6.4: Some Constructions And Inequalities For The Circle
Problem 12E
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Solve number 45
**44. Tangential Circles** Three circles with radii 1.2 inches, 2.2 inches, and 3.1 inches are tangent to each other externally. Find the angles of the triangle formed by joining the centers of the circles. *Diagram Explanation*: The image shows three tangent circles with different radii. The centers of the circles are labeled as points A, B, and C. Lines are drawn connecting these centers, forming a triangle. --- **45. Height of a Tree** A tree is planted at a point \( O \) on horizontal ground. Two points \( A \) and \( B \) on the ground are 100 feet apart. The angles of elevation of the top of the tree \( T \) from the points \( A \) and \( B \) are \( 45^\circ \) and \( 30^\circ \), respectively. The measure of \( \angle AOB \) is \( 60^\circ \). Find the height of the tree. *Diagram Explanation*: The image illustrates a triangle with a tree at point \( O \). The base \( AB \) is 100 feet. Two angle measurements, \( 45^\circ \) from \( A \) and \( 30^\circ \) from \( B \), converge at the top of the tree \( T \). The angle \( \angle AOB \) is marked as \( 60^\circ \).
Transcribed Image Text:**44. Tangential Circles** Three circles with radii 1.2 inches, 2.2 inches, and 3.1 inches are tangent to each other externally. Find the angles of the triangle formed by joining the centers of the circles. *Diagram Explanation*: The image shows three tangent circles with different radii. The centers of the circles are labeled as points A, B, and C. Lines are drawn connecting these centers, forming a triangle. --- **45. Height of a Tree** A tree is planted at a point \( O \) on horizontal ground. Two points \( A \) and \( B \) on the ground are 100 feet apart. The angles of elevation of the top of the tree \( T \) from the points \( A \) and \( B \) are \( 45^\circ \) and \( 30^\circ \), respectively. The measure of \( \angle AOB \) is \( 60^\circ \). Find the height of the tree. *Diagram Explanation*: The image illustrates a triangle with a tree at point \( O \). The base \( AB \) is 100 feet. Two angle measurements, \( 45^\circ \) from \( A \) and \( 30^\circ \) from \( B \), converge at the top of the tree \( T \). The angle \( \angle AOB \) is marked as \( 60^\circ \).
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