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Problem 12. From a point outside of an equilateral triangle, the distance to the vertices are '10-m, 10-m and 18-m. Find the dimension of the triangle.

Problem 12. From a point outside of an equilateral triangle, the distance to the vertices are '10-m, 10-m and 18-m. Find the dimension of the triangle.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Problem 11. The sides of a triangular lot are 130-m, 180-m and 190-m. The lot is to be divided by a line bisecting the longest side and drawn from the opposite vertex. What is the length of the dividing line? Problem 12. From a point outside of an equilateral triangle, the distance to the vertices are '10-m, 10-m and '18-m. Find the dimension of the triangle. Problem 13. A statue 2-m high stands on a column that is 3-m high. An observer in level with the top of the statue observed that the column and the statue subtend the same angle. How far is the observer from the statue? Problem 14. From the top of a building 100-m high, the angle of depression of a point A due East of it is 30°. From a point B due South of the building, the angle of elevation of the top is 60°. Find the distance AB. Problem 15. An observer found the angle of elevation of top of the tree to be 27°. After moving 10-m closer, the angle of elevation becomes 54°, Find the height of the tree. Problem 16. An observer wishes to determine the height of the tower. He takes sights at the top of the tower from A and B which are 50ft apart, at same elevation on a direct line with the tower. The vertical angle at point A is 30 degrees and at point B is 40 degrees. What is the height of the tower? Problem 17. From the top of tower A, the angle of elevation of the top of tower B is 46°, From the foot of tower B the angle of elevation of tower A is 28°. Both towers are on level ground. If the height of tower B is 120m, how high is tower A? Problem 18. Points A and B are 100m apart and are on the same elevation as the foot of the building. The angles of elevation of the top of the building from points A and B are 21° and 32°, respectively. How far is A from the building? Problem 19. A man finds the angle of elevation of the top of a tower to be 30 degrees. He walks 85m nearer the tower and find its angle of elevation to be 60 degrees. What is the height of the tower? Problem 20. A rectangular piece of land 40m x 30m is to be crossed diagonally by a 10m wide roadway as shown. If the land cost P1,500 per square meter, determine the cost of the roadway. 10m
Transcribed Image Text:Problem 11. The sides of a triangular lot are 130-m, 180-m and 190-m. The lot is to be divided by a line bisecting the longest side and drawn from the opposite vertex. What is the length of the dividing line? Problem 12. From a point outside of an equilateral triangle, the distance to the vertices are '10-m, 10-m and '18-m. Find the dimension of the triangle. Problem 13. A statue 2-m high stands on a column that is 3-m high. An observer in level with the top of the statue observed that the column and the statue subtend the same angle. How far is the observer from the statue? Problem 14. From the top of a building 100-m high, the angle of depression of a point A due East of it is 30°. From a point B due South of the building, the angle of elevation of the top is 60°. Find the distance AB. Problem 15. An observer found the angle of elevation of top of the tree to be 27°. After moving 10-m closer, the angle of elevation becomes 54°, Find the height of the tree. Problem 16. An observer wishes to determine the height of the tower. He takes sights at the top of the tower from A and B which are 50ft apart, at same elevation on a direct line with the tower. The vertical angle at point A is 30 degrees and at point B is 40 degrees. What is the height of the tower? Problem 17. From the top of tower A, the angle of elevation of the top of tower B is 46°, From the foot of tower B the angle of elevation of tower A is 28°. Both towers are on level ground. If the height of tower B is 120m, how high is tower A? Problem 18. Points A and B are 100m apart and are on the same elevation as the foot of the building. The angles of elevation of the top of the building from points A and B are 21° and 32°, respectively. How far is A from the building? Problem 19. A man finds the angle of elevation of the top of a tower to be 30 degrees. He walks 85m nearer the tower and find its angle of elevation to be 60 degrees. What is the height of the tower? Problem 20. A rectangular piece of land 40m x 30m is to be crossed diagonally by a 10m wide roadway as shown. If the land cost P1,500 per square meter, determine the cost of the roadway. 10m
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