Question

It is 1.9 miles from a house to a restaurant and 1.2

miles to a pier, as shown at the right. The angle
between the two lines of sight is 87°. How far is it from
the pier across the water to the restaurant.

Answer 1

9514 1404 393

Answer:

2.2 miles

Explanation:

The Law of Cosines can be used to figure this.

c² = a² +b² -2ab·cos(C)

c² = 1.2² +1.9² -2(1.2)(1.9)cos(87°) ≈ 4.811348

c ≈ √4.811348 ≈ 2.193

It is about 2.2 miles across the water from the pier to the restaurant.