Mike and Lani stand 21.2 meters apart. From Mike’s position, the angle of elevation to the top of the Eiffel Tower is 40°. From Lani’s position, the angle of elevation to the top of the Eiffel Tower is 38.5°. How many meters high is the Eiffel Tower? Round to the nearest meter.
post it.
To find the height of the Eiffel Tower, we can use trigonometry and the concept of similar triangles.
Let's call the height of the Eiffel Tower "h".
From Mike's position, the angle of elevation to the top of the Eiffel Tower is 40°. This means that the angle between the ground and the line connecting Mike's position and the top of the Eiffel Tower is 90° - 40° = 50°.
Similarly, from Lani's position, the angle of elevation to the top of the Eiffel Tower is 38.5°. This means that the angle between the ground and the line connecting Lani's position and the top of the Eiffel Tower is 90° - 38.5° = 51.5°.
Now, we can set up the following proportion:
tan(50°) = h / x (1)
tan(51.5°) = h / (21.2 - x) (2)
where x represents the distance from Mike's position to the base of the Eiffel Tower.
To find x, we can use the fact that the sum of the two distances x and (21.2 - x) is equal to the total distance between Mike and Lani, which is 21.2 meters:
x + (21.2 - x) = 21.2
21.2 = 21.2
Simplifying the equation, we get:
2x = 21.2
x = 10.6
Now, we can substitute the value of x into equations (1) and (2):
tan(50°) = h / 10.6 (1)
tan(51.5°) = h / (21.2 - 10.6) (2)
Using a calculator, we can solve these equations to find h:
tan(50°) = h / 10.6
h = tan(50°) * 10.6
h ≈ 15.1 meters
tan(51.5°) = h / (21.2 - 10.6)
h = tan(51.5°) * (21.2 - 10.6)
h ≈ 16.3 meters
The height of the Eiffel Tower is approximately 15.1 meters or 16.3 meters. Rounding to the nearest meter, the Eiffel Tower is approximately 15 meters high.
To find the height of the Eiffel Tower, we can use trigonometry. Let's denote the height of the Eiffel Tower as "h".
From Mike's position, the angle of elevation to the top of the Eiffel Tower is 40°. This means that if we draw a right triangle, the angle between the vertical height of the tower and the line connecting Mike's position to the top of the Eiffel Tower would be 40°.
Similarly, from Lani's position, the angle of elevation to the top of the Eiffel Tower is 38.5°. This means that the angle between the vertical height of the tower and the line connecting Lani's position to the top of the Eiffel Tower is 38.5°.
Now, we can set up two right triangles, one for Mike's position and one for Lani's position. The vertical height of the Eiffel Tower is the same in both triangles, which we denoted as "h".
In Mike's triangle, we have the opposite side (the vertical height of the tower) and the adjacent side (the distance between Mike and the tower). Since we know the angle of elevation (40°) and the adjacent side (21.2 meters), we can use the tangent function to find the height "h".
Using the tangent function:
tan(40°) = h / 21.2
Solving for "h":
h = tan(40°) * 21.2
Similarly, in Lani's triangle, we have the opposite side (the vertical height of the tower) and the adjacent side (the distance between Lani and the tower). Since we know the angle of elevation (38.5°) and the adjacent side (21.2 meters), we can use the tangent function again to find the height "h".
Using the tangent function:
tan(38.5°) = h / 21.2
Solving for "h":
h = tan(38.5°) * 21.2
Now, we have two values for the height "h". To find the average, we can add these values and divide by 2:
Average height = (tan(40°) * 21.2 + tan(38.5°) * 21.2) / 2
Calculating this expression will give us the average height of the Eiffel Tower. Rounding the result to the nearest meter will give us the final answer.
A = 180-40 = 140o.
B = 180-40-38.5 = 1.5o, b = 21.2 m.
C = 38.5o.
Using Law of sines:
a/sinA = b/sinB
a/sin140 = 21.2/sin1.5.
Multiply both sides by sin140:
a = 21.2*sin140/sin1.5 = 520.6 m.
h = a*sinC = 520.6*sin38.5 = 324 m.
We drew 2 rt triangles with a common ver. side, h. Line BC was drawn from top
of Bldg to the end of a hor line to form
hyp. of the larger triangle. Line BA was
drawn from top of Bldg to a point on hor. line to form hyp. of smaller triangle. AB = 21.2 m.