Determine the height of a tree which casts a shadow of 13.7m when the sun is at an angle of 28 degrees.
tan28=x/13.7
**solve for x**
13.7tan28=x
so x= approx 7.28
x = tan28 * 13.7
To determine the height of the tree, you can use the trigonometric relationship between the angle of elevation, the length of the shadow, and the height of the tree.
In this case, the angle of elevation is 28 degrees, and the length of the shadow is 13.7 meters.
Let's assume that the height of the tree is represented by 'h'. The trigonometric relationship we can use is:
tan(angle) = opposite/adjacent
In this scenario, the opposite side is the height of the tree (h), and the adjacent side is the length of the shadow (13.7 meters). Therefore, we can write the equation as:
tan(28 degrees) = h/13.7
Now, we can solve the equation to find the value of 'h'.
First, let's calculate the value of tan(28 degrees):
tan(28 degrees) ≈ 0.531
Now, we can substitute this value back into the equation:
0.531 = h/13.7
To find the height of the tree (h), we can rearrange the equation:
h = 0.531 * 13.7
Now, let's calculate the value of 'h':
h ≈ 7.2687 meters
Therefore, the height of the tree is approximately 7.2687 meters when it casts a shadow of 13.7 meters with the sun at an angle of 28 degrees.