A tree that is 10 yards tall casts a shadow 14 yards long. Find the angle of elevation from the tip of the shadow to the top of the tree. Round to the nearest degree.(1 point)
To find the angle of elevation, we can use trigonometry. The angle of elevation is the angle between the ground and the line from the tip of the shadow to the top of the tree.
We know that the height of the tree is 10 yards and the length of the shadow is 14 yards. This forms a right triangle with the tree as the hypotenuse and the shadow as the base.
Let x be the angle of elevation. Using tangent function, we have:
tan(x) = opposite/adjacent
tan(x) = 10/14
tan(x) = 0.7143
To find the angle x, we take the arctangent of 0.7143:
x = arctan(0.7143)
x ≈ 35.1 degrees
Therefore, the angle of elevation from the tip of the shadow to the top of the tree is approximately 35 degrees.