Angle of elevation type word problem please help asap

Question

From the top of a building a person spots two boats out on the lake. The angle of depression from the person to one of the boats is 54 degrees, the angle of depression from the person to the other boat is 31 degrees. How far apart are the boats if the person is 35 meters above the ground?

Answer 1

Hannah,

Again, we have two right triangles. This time, instead of being adjacent to each other and therefore additive, one is inside the other and thus we will subtract to get the difference. And because we know the vertical instead of the horizontal, we will be dividing instead of multiplying.

 

Boat one:   tan(54) = 35/dist.

 

           SO    distance = 35/tan(54) = 25.43m

 

Boat two:   tan(31) = 35/dist.

 

           SO    distance = 35/tan(31) = 58.25m

                                              ______________

subtract for distance between them = 32.82   OR     32.8 m

Answer 2

You need to find the distance each boat is from the building and then subtract them:

 

Boat 1: tan 54 = x/35

 

   x = 48.2

 

Boat 2: tan 31 = y/35

 

   y = 21

 

difference is 48.2-21 = 27.2 m apart