A girl is 160cm tall stands from the foot of a building. She finds that the angle of elevation of the top of the building is 27 degree. Calculate the height of the building to the nearest 1/2 meter. Give the solution
how far is she from the building? It appears to have been omitted.
Bla
Well, since the girl is standing at the foot of the building and looking at the top, I would say she has a pretty good view. Maybe she should consider a career in architecture!
Now, let's tackle the problem. We have the angle of elevation, which is 27 degrees, and the girl's height, which is 160cm. Using some trigonometry, we can find the height of the building.
tan(27 degrees) = height of the building / 160cm
Now, let's solve for the height of the building:
height of the building = tan(27 degrees) * 160cm
Using a scientific calculator, I found that tan(27 degrees) is approximately 0.5095.
So, the height of the building is:
height of the building = 0.5095 * 160cm = 81.52cm
But wait! We need to give the answer in meters, not centimeters. So let's convert that:
height of the building = 81.52cm = 0.8152m
Now, if we round that to the nearest half meter, the height of the building is approximately 1m.
So, the height of the building, to the nearest 1/2 meter, is 1m.
To calculate the height of the building, we can use trigonometry and the concept of similar triangles.
Step 1: Draw a diagram to represent the situation. We have a right triangle where the girl's height (160cm) is the base of the triangle, the distance from the girl to the building is the adjacent side, and the height of the building is the opposite side. The angle between the ground and the line from the girl to the top of the building is 27 degrees.
Step 2: Identify the trigonometric ratio that relates the angle we have (27 degrees) and the sides of the triangle. In this case, we are given the adjacent side (distance from the girl to the building) and we want to find the opposite side (height of the building). The trigonometric ratio that relates these sides is the tangent (tan) function.
Step 3: Apply the tangent function to calculate the height of the building. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side. Therefore, we can use the formula: tan(angle) = opposite/adjacent.
Mathematically, we can write: tan(27 degrees) = height of the building / distance from the girl to the building.
Step 4: Solve for the height of the building. Rearrange the formula to isolate the height of the building: height of the building = distance from the girl to the building * tan(27 degrees).
Plugging in the values, we have:
height of the building = distance from the girl to the building * tan(27 degrees)
= 160cm * tan(27 degrees)
Using a calculator, evaluate the tangent of 27 degrees (tan(27)) to find the value. The tangent of 27 degrees is approximately 0.5095.
height of the building = 160cm * 0.5095
= 81.52cm
Step 5: Convert the height from centimeters to meters and round to the nearest 1/2 meter. Since we want the answer in 1/2 meter increments, divide the height by 50 and round to the nearest whole number. Finally, multiply by 0.5 to get the height in meters:
height of the building in meters = (81.52cm / 50) * 0.5
= 0.82 * 0.5
= 0.41 meters
Therefore, the height of the building, rounded to the nearest 1/2 meter, is approximately 0.5 meters.