Answer :
Answer:
22.35 m
Step-by-step explanation:
Hello , I can help you with this.
Step 1
define a right triangle
height of the three: H
opposite side=
the height of the tree - 1.8 m as the horizontal should be at the height of the guard's eyes
opposite side=
H-1.8
adjacent side=distance between the guard and the tree= 9.5 m
adjacent side= 9.5 m
Hypotenuse=distance between ranger's eyes and the top of the three=C
Hypotenuse=C
α=angle between the hypotenuse and the adjacent side =65.2°
α=65.2°
Step 2
find the value of the hypotenuse with the cosine function
[tex]cos\alpha =\frac{op.side}{hypotenuse}[/tex]
put the values into the equation and solve for hypotenuse
[tex]cos\ 65.2 =\frac{9.5\ m}{hypotenuse} \\Hypotenuse=\frac{9.5\ m}{cos\ 65.2 } \\Hypotenuse=\frac{9.5\ m}{0.41}\\Hypotenuse=22.64\ m[/tex]
Step 3
find the value of the opposite side using the Pythagorean theorem
T.P
[tex]hypotenuse^{2}=adj.sede^{2}+opp.side^{2}[/tex]
solve for op.side and put the values into the equation
[tex]hypotenuse^{2}=adj.sede^{2}+opp.side^{2}\\hypotenuse^{2}-adj.sede^{2}=opp.side^{2}\\\\sqrt{hypotenuse^{2}-adj.sede^{2}} =opp.side\\opp.side=\sqrt{22.64^{2}-9.5^{2}} \\opp.side=\sqrt{422.3196}}\\op.side=20.55 m[/tex]
Step 4
use the equation opposite side=
H-1.8 to find H ( height of the three)
opposite side=
H-1.8
20.55=H-1.8
add 1.8 in both sides
20.55+1.8=H-1.8+1.8
H=22.35 m
Have a great day.