Question

An 85-foot wire is tied from the top of a utility pole to the top of the building as shown below. Find d, the distance from the pole to the building.

Answer 1

The distance from the pole to the building is 79 feet

The relationship between the utility pole and the 85-foot wire, can be adjusted to fit in the description of a right-angled triangle.

So, the distance (d) can be calculated using the following sine function.

$\sin(68) = \frac{d}{85}$

Multiply both sides of the equation by 85

$85 \times \sin(68) = \frac{d}{85} \times 85$

Cancel out the common factors

$85 \times \sin(68) = d$

Evaluate sin(68)

$85 \times 0.9272 = d$

Evaluate the product

$78.812 = d$

Approximate

$79= d$

Rewrite the equation

$d = 79$

Hence, the distance from the pole to the building is 79 feet

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