Two people are 100 feet apart on opposite sides of a tree. the angles of elevation from the people to the top of the tree are 30° and 45°. find the height of the tree. round your answer to the nearest tenth of a foot.

36.6 ft

Step-by-step explanation:

First, find the angle at the top of the tree between the people: 180° - 30° - 45° = 105°.

Next, use the Law of Sines:  

a

sin A

=  

b

sin B

=  

c

sin C

to find the distance from the top of the tree to the second person.

x

sin (30°)

=  

100 ft

sin (105°)

x ≈ 55.1689 ft

Now, you can find the height of the tree by using a 45-45-90 special right triangle, so the height =  

55.1689

2

≈ 36.6 ft

step-by-step explanation:

because 1/3 is a fraction. we can tell because there is a divisor symbol between the 1 and the 3. if we were to add 2 fractions together, we would add the numerators, which is the number on top, but not the denominators, which is the number on the bottom

1/3+1/3=2/3

hope this !