00:01
In traveling across a flat land, you see a mountain directly in front of you and this angle of elevation to the peak, it's 3 .5 degrees.
00:08
So clearly this angle is 3 .5 degrees.
00:12
Now, after you drive 11 miles, 11 miles over here, then the angle of elevation is 9 degrees.
00:21
So approximate the height of the mountain.
00:25
All right.
00:27
We will make a different separate figure over here because this is.
00:31
Consists of actually two triangles so one is the bigger triangle and one is the smaller triangle it's always a good idea to place some to make to mark the vertices over here which is a b c and d a is 3 .5 degrees and b is 9 degrees and this is 11 miles okay so the value of we are considering two triangles here and by the way, what do we have to find? the height of the mountain.
01:04
We forgot to mark it.
01:05
Let's mark it as h and let's say this is x, the unknown side length.
01:09
So in triangle b, d, c, we say that tan of 9 degrees is opposite, which is h over adjacent, which is x.
01:20
So if we cross multiply, then x will be h over tan of 9 degrees.
01:25
Let's call it equation 1.
01:28
And in triangle, in triangle, adc, adc, in fact, let's write x says 1 over tan is caught as for the reciprocal identity so this is a scot of 9 degree and let's call this one as equation 1 now we look at another triangle the bigger triangle adc so in that one tan of 35 not 35 3 .5 degrees is opposite which is h over adjacent now mind it the adjacent will be this complete length which is 11 plus x we cross multiply then 11 plus x times tan of 3 .5 degrees is h and we already have the value of x from here, which is h caught 9.
02:12
So this will be replaced with h caught 9 degrees, tan of 3 .5 degrees and that is equal to h...