A man who is 2 meters tall stands on horizontal ground. He is 32 meters from the base of a tree. The angle of elevation of the top of the tree from his line of sight is 25 degrees. What is the height of the tree to the nearest hundredth meter?

The answer should be 16.92 as the height using tangent 25 then by multiplying 32 which should be about 14.92 and then you should at the height of the man which is 2 meters and your answer should be 16.92

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apologiabiology apologiabiology · Answer 2 · 2018-04-04T07:33:29+02:00

draw diagram to help us see

as you can see, we have a right triangle with one of the legs as 32 meters

we can use trigonometry to find the height
in the 2nd picture I highlighted the sides of the triangle and labeled them a,b, and c

note that the height of the tree is the length of leg 'a' plus the height of the man or a+2

so, remember, [tex]tan(\theta)=\frac{oposite}{adjacent}=\frac{a}{b}[/tex]
the opposite side is the side opotise the angle and the adjacent side is the shorter leg next to the angle
we are given that b=32m and [tex] \theta=25^\circ[/tex]

we can solve for the value of 'a' by multilyinb both sides by b to obtain
[tex](b)(tan(\theta))=a[/tex]
input the values
[tex](32m)(tan(25^\circ))=a[/tex]
use your calculator
[tex]14.9218m=a[/tex]
now add 2 to get total height of tree
2m+14.9218m=16.9218m
now round to hundreths place
16.92m

the height of the tree to the hundreth meter is 16.92m