12 pts? harris and annabelle are 200 feet apart, and they are standing on opposite sides of a tree. the angles of elevation from harris to the top of the tree is 30°, and the angle of elevation from annabelle to the top of the tree is 35°. find the height of the tree. round your answer to the nearest tenth.

63.3

Step-by-step explanation:

First, draw a triangle with the vertices at Harris, Annabelle, and the top of the tree. Notice, the angles are 30 degrees and 35 degrees. Therefore, the missing angle is 180 - 30 - 35 = 115 degrees

If we use the law of Sines, we can determine the distance from Harris to the top of the tree, x:

X/sin(35 degrees) = 200/sin (115 degrees)

x= 200sin(35 degrees)/ sin(115 degrees)= 126.57

Now, to find the height of the tree, we can drop the altitude of the triangle and just look at the smaller triangle created with the vertices at Harris, the top of the tree, and the base of the tree. Since this is a 30 - 60 - 90 triangle with x=. 126.57 ft as the length of the hypotenuse, then the height is half of that, 63.29 ft, since it is the short leg (across from the 30 degree angle).

power property.