A communication tower is 34m tall. Jane stands somewhere in front of the tower to the right and measures the angle of elevation to be 70 degrees. Bill stands somewhere in front of the tower to the left and measures the angle of elevation to be 50 degrees. How far apart are Jane and Bill if the angle between Jane, the base of the tower and bill is 90 degrees. Round to the nearest meter.
Tan70 = 34/d1, d1 = 34/Tan70 = 12.4 m. = Jane's distance from the tower.
Tan50 = 34/d2, d2 = 34/Tan50 = 28.5 m. = Bill's distance from the tower.
d1+d2 = 12.4 + 28.5 = 40.9 m. Apart.
To solve this problem, we can use trigonometry.
Let's assume that Jane's position is represented by point A, Bill's position is represented by point B, and the base of the tower is represented by point C.
We need to find the distance between Jane and Bill, which is the length of segment AB.
First, we need to find the height of the tower (segment CD). Given that the tower is 34 meters tall, segment CD is also 34 meters.
Next, we can use the tangent function to find the lengths of segments AC and BC.
For Jane's position (point A):
tan(Angle of elevation Jane) = AC / CD
tan(70°) = AC / 34
AC = tan(70°) * 34
Similarly, for Bill's position (point B):
tan(Angle of elevation Bill) = BC / CD
tan(50°) = BC / 34
BC = tan(50°) * 34
Now we need to find the length of segment AB using the Pythagorean theorem, as we have a right triangle formed by segments AB, AC, and BC.
AB^2 = AC^2 + BC^2
AB^2 = (tan(70°) * 34)^2 + (tan(50°) * 34)^2
AB^2 ≈ (2.747 * 34)^2 + (1.191 * 34)^2
AB ≈ √(94.118 + 45.934)
AB ≈ √140.052
AB ≈ 11.833
Therefore, the distance between Jane and Bill is approximately 11.833 meters when rounded to the nearest meter.