There is lightning rod on the top of a building. From a location 650 feet from the base of the building, the angle of elevation to the top of the building is measured to be 40°.

Question

There is lightning rod on the top of a building. From a location 650 feet from the base of the building, the angle of elevation to the top of the building is measured to be 40°. From the same location, the angle of elevation to the top of the lightning rod is measured to be 44°. Find the height of the lightning rod. 

Answer 1

40 degrees angle form from ground 650 feet from building base and view to top of building

44 degree angle from same spot to top of lightening rod above the building

how tall is the building??

draw a sketch and construct triangles

solve for sides of the triangle with height of the building

use law of signs or cosines or Pythagorean Theorem

sin50/650=sin40/h

h=650sin40/sin50=about

545.4147603 feet = building height

sin44/650 = sin46/(h+r)

h+r = 650sin46/sin44 =about 673.094704 = height to top of the lightning rod

r = h+r - r = about 673 - 545 =

128 feet = length of the lightning rod

Answer 2

Draw and label a diagram.

Label the height of the building b

Label the height of the rod r

tan 40° = b / 650, solve for b

tan 44° = (b + r) / 650, solve for r by substituting value of b from above.