Can you please help me find the answer

Question

A spotlight is mounted on wall 7.4 feet above a security desk in an office building. It is used to light the entrance door 9.3 feet from the desk. To the nearest degree what is the depression from the spotlight to the entrance door. 

Answer 1

The spotlight's direct beam is focused onto what?   top of door (then what's its height)?  bottom of door (at floor level)?

 

You can answer the latter question only.  MAKE A DRAWING.  From the bottom of the floor, call that angle of elevation (line of sight up to spotlight) θ.

 

Tan θ = 7.4/9.3 ... this enables you to find the number of degrees for θ, using INVERSE TANGENT function on that ratio.

The angle of depression down to bottom of door at floor level from the spotlight is also θ.

Answer 2

From the word problem, what we have is an Imaginary triangle with 2 sides (7.4 feet and 9.3 feet) at a right angle.

 

In order to find the angle of depression, we first need to calculate the hypotenuse of the triangle.

 

Using Pythagorean theorem-----> a² +b² = c² 

 

c² = 7.4² + 9.3² 

c² =  54.76 + 86.49 = 141.25

c = 11.9 

 

Let the angle of depression be represented by x

 

cos x = adjacent/hypotenuse

 

Where adjacent = a and hypotenuse  = c

 

hence

 

cos x = 7.4/11.9  = 0.62

 

x = 52 degrees

 

 

      

Answer 3

The angle is T

 

tangent T = 9.3/7.4 = 93/74 = 1.2567567567567567.... 1.2567

 

T = 51.490771634475