Question

A guy wire that is 639.4 meters long is anchored 53.5 meters from the base of an antenna. Determine the angle the wire makes with the ground and calculate the height of the antenna. Round answers to the nearest degree and meter.

Answer 1

angle = 85 degrees

height = 637 meters

Explanation:

pythagorean theorem

a^2 + b^2 = c^2

53.5^2 + b^2 = 639.4^2

2862.25 + b^2 = 408832.36

408832.36 - 2862.25 = 405970.11

b^2 = 405970.11

`√(405970.11)`

b = 637.15

b = 637.2

so the height of the antenna is approximately 637.2 meters

to find the angle we will use trigonometric ratios

tan x = opposite/adjacent

plug in our values

tanx = 637/53.5

tanx = 11.91

arctan (11.91) = 85.2