Question

A guy wire to a tower makes a 67 degree angle with level ground. At a point 33 ft farther from the tower than the wire but on the same side as the base of the wire, the angle of elevation to the top of the pole is 38 degrees. Find the length if the wire ( nearest foot).

Answer 1

Length of the wire = 67.3 feet

Explanation:

H = height of the tower

L = length of the guy wire

sin(67 ) = H / L

H = L*sin(67)

Add 33 ft to L, and the angle is now 38 deg. So

sin(38) = H / (L + 33)

Using the 1st equation, substitute for H:

sin(38) = L* sin(67) / (L + 33)

Plug in numbers and rearrange

0.615 = L*0.920 / (L + 33)

0.615*L + 20.2 = 0.920*L

0.30*L = 20.2

L = 67.3 feet

CHECK:

H = 67.3*sin(67) = 61.94 ~ 62

H = (67.3 + 33)*sin(38) = 61.75 ~ 62

Answer 2

The length of wire is 67.3 ft.

Given data:

The angle between the tower and level ground is, $\theta = 67^{\circ}$.

The distance from the tower is, d = 33 ft.

The angle of elevation is, $\theta'=38^{\circ}$.

Let us consider the height of tower as H and length of sire be L. Then as the concept of trigonometry, the relation between the Height( vertical parameter) and Length ( horizontal parameter) is given as,

$sin\theta = \dfrac{H}{L}\\\\H = sin \theta \times L\\\\H = sin67 \times L$

Now, at 33 ft distance, the angle of elevation becomes 33 Degrees. So, the expression is,

$sin \theta' = \dfrac{H}{L+d}\\\\sin38 = \dfrac{(sin67 \times L)}{L+33}\\\\sin38(L+33)=sin67 \times L\\\\L = 67.3\;\rm ft$

Thus, we can conclude that the length of wire is 67.3 ft.

Learn more about the Trigonometric ratios here:

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