Answer to Question #133957 in Trigonometry for Muna

Question

David Beckham is attempting a goal. He is standing 52 m from one goal post and 50 m from the other. From where he is standing the angle between the goal posts is 7 degrees. Determine the width of the soccer net. Include a diagram with your solution.

Answer 1

Sketch of the above situation

Let the width of the soccer net AB be x meters

Here, we apply the cosine rule;

$a^2 = b^2 + c^2 - 2bc cos A$

In the case above; we will apply;

$c^2 = a^2 + b^2 - 2 ab cos C$

$= 50^2 +52^2 - (2 × 50 × 52) cos 7\text{\textdegree}$

$=2500 + 2704 - 5200 cos 7\text{\textdegree}$

$= 5204 - 5161.24$

$= 42.76$

$c = x =6.54$

Therefore the width of the soccer net is 6.54 meters.