Question

Jacob and Natalie are standing on a riverbank in two different spots. Both of them are looking at the same house. Natalie is 130 meters from the house. Find how far apart they are if the angle by Natalie is 40°.

a) 195 meters

b) 325 meters

c) 260 meters

d) 390 meters

Answer 1

To find the distance between Jacob and Natalie, use the sine function and the given angle of 40°. The distance between them is approximately 83.9 meters.

Step-by-step explanation:

To find the distance between Jacob and Natalie, we can use the trigonometric relationship between the angle and the distance. Since Natalie is 130 meters from the house, we can use the sine function to find the distance between Jacob and Natalie. The sine of an angle is equal to the opposite side (the distance between Jacob and Natalie) divided by the hypotenuse (the distance from Natalie to the house). Using the given angle of 40°, we can set up the equation as follows:

sine(40°) = (distance between Jacob and Natalie) / 130

Now we can solve for the distance between Jacob and Natalie:

Distance between Jacob and Natalie = sine(40°) * 130

Calculating this, we find that the distance between Jacob and Natalie is approximately 83.9 meters.