When the angle of elevation to the sun is 52 degrees, a tree casts a shadow that is 9 meters long. what is the height of the tree? round to the nearest tenth of a meter
tan52 = h/9
h = 9tan(52) = 11.5
To solve this problem, we can use trigonometry. The tangent function is defined as the ratio of the opposite side to the adjacent side in a right triangle.
Let's label the height of the tree as "h" and the angle of elevation as 52 degrees. The length of the shadow is given as 9 meters.
Using the tangent function, we can set up the equation:
tan(52 degrees) = h / 9m
Now we can solve for h:
h = 9m * tan(52 degrees)
Using a calculator, we find:
h ≈ 11.65 meters
Therefore, the height of the tree is approximately 11.65 meters.
To find the height of the tree, we can use the concept of trigonometry. The angle of elevation to the sun is 52 degrees, which represents the angle between the ground (horizontal) and the line connecting the top of the tree to the sun.
Let's denote the height of the tree as 'h'. From the given information, we know that the shadow cast by the tree is 9 meters long. This shadow represents the length of the side opposite to the angle of elevation.
By using the tangent function, we can relate the angle and the lengths of the sides of a right triangle. The tangent of an angle is equal to the ratio of the side opposite to the angle (9 meters/shadow) to the side adjacent (height of the tree/h) to the angle. Mathematically, this can be written as:
tan(52 degrees) = 9/h
Solving this equation for h, we can find the height of the tree:
h = 9 / tan(52 degrees)
Using a scientific calculator, we can evaluate the tangent of 52 degrees and then substitute it into the equation to find the height:
h = 9 / tan(52 degrees) ≈ 9 / 1.2799 ≈ 7.03 meters
Therefore, the height of the tree is approximately 7.03 meters (rounded to the nearest tenth).