Jack looks at a clock tower from a dictance and determines the the angle of elevation of the top of the tower is 40°. john who is standing 20 melters from jack as shown in the diagram, determines that the angle of elevation to the top of the tower is 60°. if jacks and johns eyes are 1.5 meters from the ground and the distance from jacks eyes to the top of the tower is 50.64 meters, how far is johns from the base of the tower?

As per the given statement:

The distance from jack eyes to the top of the tower = 50.64 m

Also, jack and john eyes are 1.5 m from the ground.

Labelled diagram as shown in the attachment

Let BC = x m  be the distance of the jack from the base of the tower and

AG = y m be the distance above 1.5 m from the the ground.

Using tangent ratio:

In triangle AGE;

Here, AG = y m and EG = 20+x m

then;

or we can write this as;

                 ........[1]

Similarly, in AGF;

then;

or

                         ......[2]

Substitute equation [2] into the equation [1], to solve for x;

or

Using distributive property:

we have;

Subtract 0.84 x from both sides we get;

Divide both sides by 0.892 we get;

Therefore, 18.8 meter johns from the base of the tower.

to find the total number of combinations, multiply the quantity of each item by each other:

2 pairs of shoes x 3 pairs of shorts = 6 different combinations.