a flagpole casts a 60 foot shadow when the angle of elevation of the sun is 35 degrees. find the height of the flagpole
tan(35°) = height of pole / shadow length.
Solve for height of pole.
To find the height of the flagpole, we can use trigonometric ratios.
Let's assume that the height of the flagpole is h.
According to the given information, the angle of elevation of the sun is 35 degrees, and the length of the shadow cast by the flagpole is 60 feet.
We can use the tangent function, which is defined as the opposite side divided by the adjacent side:
tan(angle) = opposite / adjacent
In this case, the angle is 35 degrees, the opposite side is the height of the flagpole (h), and the adjacent side is the length of the shadow (60 feet).
tan(35 degrees) = h / 60
To solve for h, we can rearrange the equation:
h = tan(35 degrees) * 60
Using a calculator, we can find that tan(35 degrees) is approximately 0.7002. Multiplying this by 60 feet, we get:
h ≈ 0.7002 * 60 ≈ 42.01 feet
Therefore, the height of the flagpole is approximately 42.01 feet.
To find the height of the flagpole, we can use the trigonometric relationship between the angle of elevation, the height, and the shadow. In this case, the tangent function will be helpful.
Let's denote the height of the flagpole as "h" (in feet). We are given that the angle of elevation of the sun is 35 degrees, and the length of the shadow is 60 feet.
Tangent is defined as the ratio of the opposite side (the height of the flagpole, h) to the adjacent side (the length of the shadow, 60 feet).
Using the tangent function, we have:
tan(35 degrees) = h / 60
To solve for h, we can rearrange the equation as follows:
h = tan(35 degrees) * 60
Now, let's calculate the value of h using a calculator:
h ≈ tan(35 degrees) * 60
h ≈ 0.7002 * 60
h ≈ 42.012 feet
Therefore, the height of the flagpole is approximately 42.012 feet.