Question
A 127 foot tower is located on hill that is inclined 38° to the horizontal. A guy wire is to be attached to the top of the tower and anchored at a point 64 feet downhill from the base of the tower. Find the length of wire needed.
Answers
law of cosines
x² = 127² + 64² - [2 * 127 * 64 * cos(90º + 38º)]
x² = 127² + 64² - [2 * 127 * 64 * cos(90º + 38º)]
bobpursley
draw the figure.
Label tower 127', then from the top of tower to the 64 mark downill, length L, draw a horzontal from the 64 mark, and then the height from the horizonal line to the FOOT of the tower as A.
Label the angles.
Note the angle formed by the hill and the base of the tower (the internal angle)can be determined from the vertical line through the base: Angleinternal = 90+38 Think that out.
So, you have two sides of on the guy wire triangle L, and 127, and 64.
You have SAS. use the law of cosines:
L^2=127^2+64^2-2*127*64*CosAngleinternal. solve for L
Label tower 127', then from the top of tower to the 64 mark downill, length L, draw a horzontal from the 64 mark, and then the height from the horizonal line to the FOOT of the tower as A.
Label the angles.
Note the angle formed by the hill and the base of the tower (the internal angle)can be determined from the vertical line through the base: Angleinternal = 90+38 Think that out.
So, you have two sides of on the guy wire triangle L, and 127, and 64.
You have SAS. use the law of cosines:
L^2=127^2+64^2-2*127*64*CosAngleinternal. solve for L