Question

a guy wire makes a 67 degree angle with the ground. walking out 32 ft further grom the tower,the angle of elevation to the top of the tower is 39 degrees. find the height of the tower

Answer 1

Answer:

  39.5 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relation between angles and sides of a right triangle.

  Tan = Opposite/Adjacent

This lets us write two equations in two unknowns:

  tan(67°) = AD/CD . . . . . . . . . . angle at guy point

  tan(39°) = AD/(CD+32) . . . . . .angle 32' farther

__

Solving the first equation for CD and using that in the second equation, we can get an equation for AD, the height of the tower.

  CD = AD/tan(67°)

  tan(39°)(CD +32) = AD . . . . eliminate fractions in the second equation

  tan(39°)(AD/tan(67°) +32) = AD

  32·tan(39°) = AD(1 -tan(39°)/tan(67°)) . . . simplify, subtract left-side AD term

  32·tan(39°)tan(67°)/(tan(67°) -tan(39°)) = AD . . . . divide by AD coefficient

  AD ≈ 39.486 . . . . feet

The tower is about 39.5 feet high.