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

the image of (6, 9) under a dilation is (4, 6). the scale factor is

function 2 has a greater rate of change than function 1

function 2 has a greater y-intercept than function 1

step-by-step explanation: