A platform and building are on thesame plane. The of angle of depression of the bottom(c) of the building from the top(a) of the platform is 39degree. The angle of elevation of the top(o)of the building from the top of the platform is 56. Given that the distance between the foot of the platform and that of the building is 10meters, calculate the height of the building to the nearest whole number
It is hard to decipher your wording but I will try.
Let a parallel line from the top of the platform meet the height of the building at C
Label the top of the building A, and its bottom as B
tan56° = AC/10 --> AC = 10tan56
tan39° = BC/10 --> BC = 10tan39
height of building
= AC + BC
= 10tan56 + 10tan39
= ...
To solve this problem, we can use the principles of trigonometry, specifically the tangent function.
Let's call the height of the building "h" and the distance from the top of the platform to the building's base "d".
First, we need to find the value of angle b, which is the angle of elevation of the top of the building from the bottom of the building (angle b + angle c = 90 degrees).
Using the property of angles on a straight line, we know that the sum of all angles on a straight line is 180 degrees. Therefore, angle b + angle o = 180 degrees.
Now, let's solve for angle b:
angle b = 180 degrees - angle o
angle b = 180 degrees - 56 degrees
angle b = 124 degrees
Now we have all the angles: angle c = 39 degrees, angle b = 124 degrees, and angle o = 56 degrees.
Next, we can use the tangent function to find the height of the building:
tan(angle c) = opposite side / adjacent side
tan(39 degrees) = h / d
We need to find the value of d, the distance between the platforms' foot and the building's foot. Given in the problem, this distance is 10 meters.
So, we have an equation:
tan(39 degrees) = h / 10
Now we can solve for h:
h = 10 * tan(39 degrees)
h ≈ 10 * 0.8097840331950078
h ≈ 8.1 (rounded to one decimal place)
Therefore, the height of the building is approximately 8 meters (rounded to the nearest whole number).