Question

a town park has two paths leading to the playground. one path is 2 miles from the road and the other path makes a right angle with the road. the two paths intersect at an angle of 50°. what is the approximate distance from the playground to the road along the other path?
a. 1.5 mi
b. 1.3 mi
c. 3.1 mi
d. 2.6 mi

Explanation:

Step1: Identify trigonometric ratio

The triangle is right-angled, with hypotenuse 2 mi, angle 50°, and the required side is adjacent to the angle. Use cosine: $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$.

Step2: Calculate adjacent side

Rearrange: $\text{adjacent} = 2 \times \cos(50^\circ)$. $\cos(50^\circ) \approx 0.6428$.

Step3: Compute the value

$2 \times 0.6428 \approx 1.2856 \approx 1.3$ mi.

Answer:

B. 13m (Note: Likely a unit typo; should be 1.3 mi, matching option B's value)