From the top of a building 70 ft. high, two objects in a straight line from the building are observed at angles of depression of 28° and 41°6' respectively. Find the distance between the two objects.
-Complete Solution please. :'(
The distances to the objects (assumed to be at ground level) are
H/tan28 and H/tan41.1,
where h = 70 feet.
70/tan28 - 70/tan41.1 = 131.65 - 80.24
= 51.41 feet
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IF MICHLLE IS FLYING A KITA ON 35 METRE STING THAT MAKES AN ANGLE OF 56 DEGREES WITH THE HORIZONTAL CALCULATE THE HEIGHT OF THE KITE TO THE NEAREST METRE
To find the distance between the two objects, we need to use trigonometry.
Let's label the height of the building as h = 70 ft. We want to find the distance between the two objects.
First, let's find the distance between the building and the first object. We can use the tangent function.
tan(28°) = h / x1
where x1 is the distance between the building and the first object.
Rearranging the equation, we have:
x1 = h / tan(28°)
Let's plug in the values:
x1 = 70 / tan(28°)
Using a calculator, we find that tan(28°) ≈ 0.5317:
x1 = 70 / 0.5317
≈ 131.66 ft
So, the distance between the building and the first object is approximately 131.66 ft.
Now, let's find the distance between the building and the second object. We can use the same process using the angle of depression of 41°6'.
tan(41°6') = h / x2
where x2 is the distance between the building and the second object.
Rearranging the equation, we have:
x2 = h / tan(41°6')
Let's convert 41°6' to decimal degrees:
41°6' = 41 + 6/60 ≈ 41.1°
Now, let's plug in the values:
x2 = 70 / tan(41.1°)
Using a calculator, we find that tan(41.1°) ≈ 0.8504:
x2 = 70 / 0.8504
≈ 82.31 ft
So, the distance between the building and the second object is approximately 82.31 ft.
Finally, to find the distance between the two objects, we can subtract the distances between the building and each object:
Distance between the two objects = x1 - x2
Distance between the two objects ≈ 131.66 ft - 82.31 ft
≈ 49.35 ft
Therefore, the distance between the two objects is approximately 49.35 ft.