Answer
The height of the tree is 53.2 feet
Work Step by Step
Let C be the point at the top of the tree.
Let D be the point where the angle of elevation is $27.2^{\circ}$
Let E be the point level with point D which is directly under the tree.
Then points CDE form a triangle. We can find the angle $C$:
$C+D+E= 180^{\circ}$
$C = 180^{\circ}-D-E$
$C = 180^{\circ}-27.2^{\circ}-90^{\circ}$
$C = 62.8^{\circ}$
Let C be the point at the top of the tree.
Let B be the point at the bottom of the tree
Let A be the point where the angle of elevation is $14.3^{\circ}$. Then from point A, the angle between the bottom of the tree and the top of the tree is $27.2^{\circ}-14.3^{\circ} = 12.9^{\circ}$
The points ABC form a triangle. We can use the law of sines to find $h$, the height of the tree:
$\frac{h}{sin~12.9^{\circ}} = \frac{212~ft}{sin~62.8^{\circ}}$
$h = \frac{(212~ft)~sin~12.9^{\circ}}{sin~62.8^{\circ}}$
$h = 53.2~ft$
The height of the tree is 53.2 feet
