if the angle of elevation of the sun with the ground is 10 degrees, what is the length of a shadow cast by a six foot person to the nearest foot?
x/6 = cot 10°
x = 34 ft
To find the length of the shadow cast by a six-foot person, we can use the concept of trigonometry and the given angle of elevation. Here's how we can calculate it:
Step 1: Make a right triangle. Let's assume the person's height is the vertical side of the triangle, the length of the shadow is the horizontal side, and the line from the top of the person's head to the tip of the shadow is the hypotenuse.
Step 2: Since we have the angle of elevation and the vertical side (person's height), we can use the tangent function, which is defined as the ratio of the opposite side (shadow's length) to the adjacent side (person's height).
Step 3: Apply the tangent function: tan(angle of elevation) = opposite/adjacent. In this case, tan(10 degrees) = shadow length/6ft.
Step 4: Solve for the shadow length. Multiply both sides of the equation by 6ft:
shadow length = 6ft * tan(10 degrees).
Step 5: Use a calculator to find the approximate value of tan(10 degrees) and calculate the shadow length.
By following these steps, you can find the length of the shadow cast by the six-foot person to the nearest foot.