1. From a point 15m from the base of a tree, the angle of elevation of the top of the tree is 46.48degrees. Approximate the height of the tree.
2. From a point 17.2m from the base of a building, the angle of elevation of the top of the building is 73.5degrees. Aproximate the height of the building.
Looks like you need to review the basic trig functions and draw useful diagrams.
#1 h/15 = tan 46.48°
#2 h/17.2 = tan 73.5°
To solve both problems, we can use trigonometry, specifically the tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side. In these cases, the opposite side is the height of the tree or building, and the adjacent side is the distance from the tree or building.
1. To approximate the height of the tree:
We have the following information:
Distance from the base of the tree (adjacent side) = 15m
Angle of elevation = 46.48 degrees
Using the tangent function, we can set up the equation:
tan(46.48) = height / 15
Now we can solve for the height:
height = 15 * tan(46.48)
Calculating this, we find that the height of the tree is approximately 16.8m.
2. To approximate the height of the building:
Similarly, we have the following information:
Distance from the base of the building (adjacent side) = 17.2m
Angle of elevation = 73.5 degrees
Using the tangent function again, we set up the equation:
tan(73.5) = height / 17.2
Solving for the height:
height = 17.2 * tan(73.5)
Calculating this, we find that the height of the building is approximately 52.9m.