A tower casts a 235-foot-long shadow. If the angle of elevation from the tip of the shadow to the top of the tower is 66.3°, how high is the tower? (Round your answer to one decimal place.)
h/235 = tan 66.3°
h = 235 (tan 66.3°)
= ....
you do the button-pushing, make sure your calculator is set to degrees.
To find the height of the tower, we can use trigonometry, specifically the tangent function. The tangent of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
In this case, the height of the tower is the side opposite the angle of elevation, and the length of the shadow is the side adjacent to the angle. So we have:
tan(theta) = opposite / adjacent
Here, theta represents the angle of elevation, opposite represents the height of the tower, and adjacent represents the length of the shadow.
Plugging in the values we have:
tan(66.3°) = opposite / 235
We can now solve for the height of the tower by rearranging the equation:
opposite = tan(66.3°) * 235
Using a calculator or a software, we can evaluate the right side of the equation to get the height of the tower:
opposite ≈ 544.0 feet
Therefore, the height of the tower is approximately 544.0 feet.