Question

The angle of elevation of the top of an unfinished tower at a point is 80 m from the base is 30 degrees.How much higher must be the tower to be raised so that its angle of elevation at the same point be 60 degrees?

Answer 1

@Kainui

Answer 2

@mashy

Answer 3

Try drawing a picture, something like:

Answer 4

The point they're talking about is the left-most point of the triangle, and the base would be 80m.
First, using simple trig, find x.
Then, find (h+x) using the same technique.
Your answer is whatever h is.

Answer 5

???

Answer 6

Which part is confusing you?

Answer 7

The whole thing :/

Answer 8

Ok so you have this originally:

Answer 9

Your first mission is to find x, the height of the unfinished tower.
Which trig function will you use - sin, cos or tan?

Answer 10

\[\tan 30 = \frac{ x }{ 80 }\]
Can you see why that is true? Rearrange that to find x.

Answer 11

Then you can redraw the situation as such and use the same technique to find x + h.

However, we don't want the height of the final tower, we want the difference between their heights - and that would be (x + h) - x = h.

Answer 12

80/sqrt3 = x?

Answer 13

That seems right :)

Answer 14

I have been told to use 1.732 when I came across sqrt3
So I mean is
80/1.732 = x?

Answer 15

Well, I would say it's better to use exact values, but if you want to round your answer to the nearest metre then yeah, x is approximately equal to 80/1.732 (and you can chuck that into your calculator to work it out).

Answer 16

But the final answer we're looking for is h. So what will it be and how do we get there?

Answer 17

Alright.

Answer 18

is x 46.18 m?

Answer 19

x = 46.18802154... = 46.19m (to 2 decimal places, if that's what you want).
In maths you normally want to use exact values ( like 80/sqrt(3)) until your final answer, which you can round.

Answer 20

sqrt3 = (46.19 + h)?

Answer 21

@perl @Tommynaut

Answer 22

Did you get that with a trig calculation? What did you do with the 80?

Answer 23

5.9?