Angle of elevation from the sun is 45 degree.a tree has a shadow 12m long.find the height of this tree.
draw a diagram, and you can see that
h/12 = tan45°
Why did the tree go to the sunbathing salon? Because it wanted to get a little higher!
But in all seriousness, let's solve this problem. We have the angle of elevation from the sun as 45 degrees and the length of the tree's shadow as 12 meters. To find the height of the tree, we can use basic trigonometry.
The tangent of the angle of elevation is equal to the height of the tree divided by the length of its shadow. So, tan(45°) = height/12m.
Using a calculator, we find that the tangent of 45 degrees is 1. Therefore, height/12m = 1.
To find the height, we can multiply both sides of the equation by 12m:
height = 1 * 12m,
height = 12m.
So, the height of the tree is 12 meters.
To find the height of the tree, we can use the concept of trigonometry. We need to create a right triangle with the tree, its shadow, and the sun.
Let's label the height of the tree as 'h' (which we want to find) and the length of the shadow as 's' (given as 12m). To find the height, we can use the tangent function.
We know that the angle of elevation from the sun is 45 degrees. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side. In this case, the opposite side is the height of the tree 'h', and the adjacent side is the length of the shadow 's'.
The tangent of an angle can be calculated by dividing the opposite side by the adjacent side:
tan(angle) = opposite/adjacent
tan(45°) = h/12
Now, let's solve for 'h':
h = 12 * tan(45°)
To calculate this value, we can use a scientific calculator or table of trigonometric functions.
Using a scientific calculator, we find:
h ≈ 12 * 1
So, the height of the tree is approximately 12 meters.
To find the height of the tree, we can use the trigonometric concept of the tangent function.
Let's denote the height of the tree as "h". We know that the angle of elevation from the sun is 45 degrees, and the length of the shadow is 12 meters.
The tangent of an angle is equal to the ratio of the opposite side length to the adjacent side length. In this case, the opposite side is the height of the tree (h), and the adjacent side is the length of the shadow (12m).
Using the tangent function, we can set up the following equation:
tan(45 degrees) = h / 12
The tangent of 45 degrees can be simplified as 1, so the equation becomes:
1 = h / 12
To solve for h, we can multiply both sides of the equation by 12:
12 * 1 = 12 * (h / 12)
12 = h
Therefore, the height of the tree is 12 meters.