A platform and a building are on thesame plane. The angle of depression of the bottom(c) of the building from 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 of the building is 10meters, calculate the height of the building to the nearest whole number
The errors in your problem makes it difficult to understand.
the answer is 16m.
To solve this problem, we can use trigonometry and create a diagram to visualize the situation.
Let's label the diagram:
- The bottom of the building (point C)
- The top of the building (point O)
- The foot of the platform (point A)
- The angle between the line from A to C and the horizontal line is 39 degrees, which is the angle of depression of point C.
- The angle between the line from O to the platform and the horizontal line is 56 degrees, which is the angle of elevation of point O.
- The distance between A and C is 10 meters.
Now, let's define some trigonometric ratios:
- Tan(angle) = opposite / adjacent
- Opposite refers to the side opposite to the given angle.
- Adjacent refers to the side adjacent (next to) the given angle.
In this case, if we consider triangle AOC:
- Tan(39 degrees) = OC / CA
- OC is the height of the building, which is what we want to find.
- CA is the distance between A and C, which is 10 meters.
Similarly, if we consider triangle AOB:
- Tan(56 degrees) = OC / OA
- OC is the height of the building, which is what we want to find.
- OA is the distance between A and O. However, we don't have the value for OA.
To find the height of the building, we have two equations with two unknowns (OC and OA). We can solve this system of equations simultaneously.
First, let's solve the equation from triangle AOC:
Tan(39 degrees) = OC / 10
OC = 10 * Tan(39 degrees)
OC ≈ 10 * 0.809 = 8.09 meters (rounded to two decimal places)
Next, let's solve the equation from triangle AOB:
Tan(56 degrees) = OC / OA
OA = OC / Tan(56 degrees)
OA = 8.09 / Tan(56 degrees)
OA ≈ 8.09 / 1.499 = 5.397 meters (rounded to three decimal places)
Finally, we have found the value of OA, which is the distance between A and O.
The height of the building (OC) is already calculated as 8.09 meters.
Therefore, the height of the building to the nearest whole number is approximately 8 meters.