# TRIGONOMETRY Problem

Running Header: TRIGONOMETRY PROBLEM 1

TRIGONOMETRY

Problem

Thetop two contenders for the Premier League title this season arefacing each other. The teams are indicated as Chelsea Fc and Tottenham Hotspur. Chelsea is confronted with a counterattack from Tottenham. Harry Kane is the player initiating the counterattack and isrunning towards the goal post at an angle of 41 degrees with a speedof 40km/hr. On the opposite side, Willian is running verticallystraight towards the goal post at a speed of 30km/hr. William expectsto defend his team from a goal by blocking Harry Kane`s strike. Thedistance between Willian and the goal post is 68 meters.

a).Will Harry Kane be able to strike before Willian gets hold of him?

b).Who will be late and by how long?

Thediagram below represents the situation occurring from the statedtrigonometry question. The hypotenuse represents Kane’s distancefrom the goal post. The opposite side represents William’s distancefrom the goal post. The solution to this trigonometric question iscalculated below.

Solution

Thedistance between Harry Kane and the goal post will be,

Sin(x)= opposite/hypotenuse

Theformula will lead to the formation of an equation workable throughthe angle and distance as indicated on the diagram. Therefore, x willbe 41 while the opposite side is 68 meters.

Sin(41) = 68/h

h=68/sin(41) = 103.65m

(40km/hr.)* (1000m/3600s) = 11.11m/s

Toget to the goal post Kane will take:

(103.65/11.11)= 9.33 seconds

ForWilliam,

(30km/hr.)* (1000/3600) = 8.33m/s

Toget to the goal post William will take:

(68/8.33)= 8.16 seconds

a).Therefore, Harry Kane will be able to make the strike before Williamgets hold of him.

b).William will be late by,

(9.33-8.16)= 1.17 seconds

Reference

Young,C. (2016). *Trigonometry*(1st ed.). [Place of publication not identified]: John Wiley.

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