By setting up a right triangle and applying trigonometry, the building's height is approximately 153.7 meters (from a 33° angle) or 96.4 meters (from a 46° angle).
Here's how to find the height of the building:
Set up the geometry: Imagine the situation as a right triangle, where the building is the vertical leg, the distance between the two points where the angles are measured is the horizontal base, and the angles of elevation are opposite the corresponding legs.
Use trigonometry: Since you have two angles and the base length, you can use the tangent function (tan) to solve for the missing leg (the height of the building).
Calculate the height:
For the first angle (33°), calculate the tangent: tan(33°) ≈ 0.649.
Divide the base length by the tangent: 100 m / 0.649 ≈ 153.7 m.
Repeat the same steps for the second angle (46°): tan(46°) ≈ 1.036, and 100 m / 1.036 ≈ 96.4 m.
Therefore, the height of the building is approximately 153.7 meters (using the first angle) or 96.4 meters (using the second angle).
Complete question:
To measure the height of a building, the angles of elevation are measured from two points 100m apart. What is the height if the angles are 33° and 46°?