Nadia is standing 60 ft from a tower. The angle of elevation from where she is standing on the ground to the top of the tower is

Question

algol [13]

3 years ago

5

Nadia is standing 60 ft from a tower. The angle of elevation from where she is standing on the ground to the top of the tower is

30 degrees. How tall is the tower?

Mathematics

1 answer:

torisob [31] · Answer 1 · 2022-04-25T05:45:15+03:00

This is all about right triangles, assuming the tower is not the leaning tower of pisa! The tower is our height of the right triangle, the base of our triangle is the distance Nadia is from the tower, and the reference angle is 30 (the base angle that is NOT the right angle). The tower is opposite this reference angle, and the side 60 is adjacent to this angle, so we will use the tangent ratio, the trig identity that relates the side opposite the reference angle to the side adjacent to it. $tan(30)= \frac{x}{60}$ . Solving for x we get x = 60 tan(30°). On our calculators that gives us that x = 34.64. That's how tall the tower is.