B. Tom and Sam are on the opposite sides of a building (they are outside the building) of 160 meters

height. They measure the angle of elevation of the top of the tower as 40° and 55° respectively. If the

building is 50 meters wide, find the distance between Tom and Sam.

The distance between Tom and Sam is about 352.37m.

Step-by-step explanation:

We can answer this question using Trigonometry.

Firstly, we need to draw all the information given in the question:

We attached a graph containing all this information (see below).

Having the elevation angles, the building height and width, from graph below, we can determine that the total distance is:

Where

.

.

Knowing from Trigonometry that the tangent of an angle is defined as:

Then

And

The opposite side of is the height of the building (160m). The same is the case for the opposite side of , that is, the height of the building too.

The adjacent side for is and for is .

The value of the tangent for an angle (alpha, in this case) = 40 degrees, rounding it to two decimals places is about: tan(40) = 0.84.

The value of the tangent for an angle (beta, in this case)= 55 degrees, rounding it to two decimals places is approximately: tan(55) = 1.43.

Then

Solving the equation for the distance from Tom to the building:

For calculating Sam's distance from the building, we can proceed following the same steps:

So

The distance between Tom and Sam is the resulting value of the sums:

Thus, The distance between Tom and Sam is about 352.37m.

See the graph below.

(Note: without rounding the respectives values for tangent of each angle, the value for the distance is about 352.71m).

answer: the correct answer is -32

step-by-step explanation: