Two homes are located on opposite sides of a small hill See

Two homes are located on opposite sides of a small hill. See the illustration. To measure the distance between them surveyor walks 50 feet from house P to point R, uses a transit to measure PRQ, which is found to be 80degree, and then walks to house Q, a distance of 60 feet. How far apart are the houses to the nearest hundreth?

Solution

Looking at the triangle we have two sides and angle between the two

sides given.We have to find the lenght of side opposite to it

Apply cosine rule:

PQ^2 = PR^2 +RQ^2 -2PR*RQcos80

PQ^2 = 50^2 +60^2 -2*50*60cos80

PQ = 71.12 ft

The two houses are 71.12 feet apart