A pine tree casts a 12-meter shadow on level ground. The angle of elevation from the tip of the shadow to the top of the tree is 50 degrees. To the nearest tenth of a meter, what is the height of the pine tree? Explain
thank you!
To find the height of the pine tree, we can use trigonometry and the concept of similar triangles.
First, let's label the given information on a diagram:
Let "h" represent the height of the pine tree.
The length of the shadow is given as 12 meters.
The angle of elevation from the tip of the shadow to the top of the tree is 50 degrees.
Now, we can set up a right triangle with the pine tree, its shadow, and the tip of the shadow as the vertices.
Using the angle of elevation, we know that the tangent of the angle is equal to the opposite side (height of the pine tree, h) divided by the adjacent side (length of the shadow, 12m).
So, we can set up the equation: tan(50°) = h/12
To solve for h, we can multiply both sides of the equation by 12: h = 12 * tan(50°)
Using a scientific calculator or the trigonometric function on a calculator, we can find the tangent of 50 degrees.
h ≈ 12 * 1.1918
h ≈ 14.3
So, the height of the pine tree is approximately 14.3 meters.
a simple trig problem
tan 50º = h/12
h = 12tan50
= ....