Question

Faith stands in her backyard and watches her children play. Nadia is 60 feet away in the sandbox.

Answer 1

Answer: Nadia and Jolene are 160.3 feet apart.

Step-by-step explanation: Please refer to the picture attached for more details.

Based on the information provided, the diagram has been sketched to show Faith standing at point F, and Nadia is 60 feet away at point N. Faith now turns and forms an angle measuring 130 degrees to look at Jolene who is 115 feet away from Faith. The distance between Nadia and Jolene which is line NJ is yet unknown.

What we now have is an obtuse angled triangle with one angle and two sides given. We shall solve for the unknown side using the cosine rule as follows;

a² = b² + c² - 2bcCosA

Substituting for the values of a, b and c as x, 60 and 115, the formula now becomes;

x² = 60² + 115² - 2(60)(115)(Cos 130)

x² = 3600 + 13225 - 13800(-0.6428)

x² = 16825 + 8870.64

(Note that when two negative values multiply each other the answer is positive, that is -13800 x -0.6428 = 8870.64)

x² = 25695.64

Add the square root sign to both sides of the equation

√x² = √25695.64

x = 160.298596

x ≈ 160.3 feet (rounded to the nearest tenth of a foot)