A tree 19 feet tall casts a shadow which forms an angle of 49° with the ground. How long is the shadow to the nearest hundredth
L = 19 / sin49 = 25.18 Ft.
To find the length of the shadow, we can use the tangent function. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
In this case, the angle formed between the tree and its shadow is 49°, and the height of the tree is the opposite side, while the length of the shadow is the adjacent side.
Let's denote the length of the shadow as "x".
Using the tangent function, we have:
tan(49°) = height of the tree / length of the shadow
tan(49°) = 19 / x
To solve for "x", we need to isolate it. We can do this by rearranging the equation:
x = 19 / tan(49°)
Now we can plug in the numbers to calculate the length of the shadow:
x ≈ 19 / tan(49°)
Using a scientific calculator:
x ≈ 19 / 1.1918 ≈ 15.96
Therefore, the length of the shadow to the nearest hundredth is approximately 15.96 feet.