Answer :
Answer:
x = 190.9 ft
y = 260.4 ft
z = 190.9 ft
Step-by-step explanation:
You want the values of x, y, and z in the geometry shown.
Isosceles right triangle
The lengths marked x and z are the legs of an isosceles right triangle with hypotenuse 270 ft. We know the ratio of the side lengths of such a triangle is ...
1 : 1 : √2
so ...
x = z = 270/√2 ≈ 190.9 . . . feet
Tall wall
The part of y that lies below the observation point has measure x.
The part of y that lies above the observation point can be found using the tangent relation:
Tan = Opposite/Adjacent
tan(20°) = (y-x)/z
Solving for y and using x=z, we have ...
z·tan(20°) = y -z . . . . . . multiply by z
z(1+tan(20°) = y . . . . . . add z
[tex]y=\dfrac{270}{\sqrt{2}}(1+\tan(20^\circ))\approx260.4[/tex]
The tall wall (y) is about 260.4 feet high.