Question

A dog has a 25 ft leash attached to a corner where a garage and fence meet. When the dog pulls the leash tight and walks from the fence to the garage, the arc the leash makes is 74.3 ft. What is the measure of the angle between the garage and fence, in degrees?

150 degrees
170 degrees
190 degrees
107 degrees

Answer 1

Answer: $170^{\circ}$

Step-by-step explanation:

Given

The dog has a 25 ft leash

Arc length is 74.3 ft

Arc length is given by

$l=\dfrac{\theta }{360^{\circ}}\times 2\pi r$

here, r=25 ft

l=74.3 ft

Put the values

$\Rightarrow 74.3=\dfrac{\theta }{360^{\circ}}\times 2\pi \times 25\\\\\Rightarrow \theta =170.2^{\circ} \approx 170^{\circ}$

The measure of the angle is  $170^{\circ}$