The bearing of a house from a point A is 319.From a point B ,317m due east of A.The bearing of the house is 288°.How far is the house from A?
To find the distance between point A and the house, we can use trigonometry.
Step 1: Draw a diagram to represent the situation. Let's call the house H, point A, point B, and the distance from A to H, d.
Step 2: Using the given information, we know that the bearing of the house from point A is 319°, and the bearing of the house from point B is 288°.
Step 3: Since the bearing is given as an angle clockwise from north, we can determine the angle between line segment AB and line segment AH.
This angle is given by (360° - 288°) = 72°.
Step 4: Since this angle is the same as the angle between line segment AH and the horizontal, we can use trigonometry to find the length of line segment AH.
Using the angle and the known length of AB (317m), we can use the trigonometric function tangent.
tan(72°) = d/317
Solving for d:
d = tan(72°) * 317
Using a calculator, we find that d is approximately equal to 887.24 meters.
Therefore, the distance from point A to the house is approximately 887.24 meters.