Question

The diagram below, not drawn to scale, shows two ships R and S at anchor on a lake of calm water. FT is a vertical tower. FSR is a straight line and RS = 150m. The angles of elevation of T, the top tower, from R and S are 22 degrees and 40 degrees respectively. F is the foot of the tower. What is the height of tower FT

Answer 1

Answer:

The answer i have got (for the height of FT) is 50.8 or 50.85 metres in length.

Step-by-step explanation:

I suspect this question is associated to trigonometry so here is how i would solve it (hopefully) successfully. Correct me if I'm wrong, i hope this helped anyways! <3

Step 1: FTR is the whole triangle (as you can see) but it is divided into two triangles. The one we are focusing on first is triangle STR. We must look at the edge RS first which is 150m in length and corner R is a 22 degree angle. Now lets look at the opposite/adjacent side of corner/angle R, which is the side that triangle STR shares with the other triangle FTS. Lets call this the 'Adjacent edge ST/TS.' We want to find the length of the 'Adjacent edge ST'. We do this by using the trig ratio- tangent. The formula is:

Tan R (Angle/Corner R)= opposite/adjacent.

So we substitute Angle R with 22 (for 22 degree angle) and substitute adjacent with 150m. (We leave 'opposite' as value b.)

Our formula now looks like this: Tan 22= b ÷ 150 (WERE NOT DONE YET!)

Now if we want to move 150 to the other side we have to multiply it to both sides! So it becomes:

150 × tan 22= b

Find your calculator and put this equation into it... the answer is 60.6m, therefore 'Adjacent edge ST' or edge ST is equal to 60.6m.

(PHEW... This step was a bit too long- but you can break it up if you feel like it :))

Final Step (Step 2): We are finally left with another length. This last step is really easy because we must simply repeat are actions from the last step.

Copy the formula but substitute the 150m for 60.6m and tan22 with tan40.

The formulae looks like this:

1. Tan S= opposite/ adjacent
2. Tan 40 (°)= b ÷ 60.6
3. 60.6 × tan 40= b
4. 60.6 × tan 40= 50.8 or 50.85

Again this can only work with a calculator and you only need to put the 3rd formula into the calculator to get 50.8/5.

We have come to an conclusion that 50.85m which is the height of tower FT of the diagram. Hope this made sense, thank you for asking! Pls add me to brainliest if you think this helped at all!