A tree on a hillside casts a shadow 215 ft down the hill. If the angle of inclination of the hillside is 22 degree to the horizontal and the angle of elevation of the sun is 52 degreess, find the height of the tree.
TIA
sorry this is law of sines. sorry for the confusion.
51235
No problem! We can use the Law of Sines to solve this problem. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant. So, let's label our triangle:
We have a right triangle with the hillside as the hypotenuse (denoted as H), the height of the tree as the side opposite the angle of inclination (denoted as h), and the shadow length as the side opposite the angle of elevation of the sun (denoted as s).
Now, let's set up the equation using the Law of Sines:
sin(angle of elevation) = h / H
sin(52) = h / 215
To find the height of the tree (h), we need to isolate it in the equation. Multiply both sides of the equation by 215:
215 * sin(52) = h
h ≈ 170.64 ft
Therefore, the height of the tree is approximately 170.64 ft.