Determine the height of a tower if it casts a shadow 156 ft long on level ground when the angle of elevation of the sun is 20°. (Round your answer to the nearest hundredth)
h/156 = tan 20°
now solve for h
To determine the height of the tower, we can use the trigonometric relationship between the angle of elevation, the length of the shadow, and the height of the tower. In this case, we have the angle of elevation as 20° and the length of the shadow as 156 ft.
Let's use the tangent function, which relates the opposite side (height of the tower) to the adjacent side (length of the shadow):
tan(angle) = opposite/adjacent
Plugging in the values we know into the equation, we get:
tan(20°) = height/156
Now, to isolate the height, we can rearrange the equation:
height = tan(angle) * adjacent
height = tan(20°) * 156
Using a scientific calculator or trigonometry tables, we find that tan(20°) ≈ 0.3640. By substituting this value into our equation, we can calculate the height:
height ≈ 0.3640 * 156
height ≈ 56.784
Therefore, the height of the tower is approximately 56.78 ft.