# Question #023a8

##### 1 Answer

(i)

(ii)

(iii)

(iv)

#### Explanation:

I assume that I can use a calculator for this because 25 degrees is not really a great number to work with in trigonometry. I will also ignore the [ ] (brackets) and | | (pipes) notations.

Okay, let's do this.

(i) Consider the triangle ABT.

We know the following relation:

so

which is

(ii) Consider the triangle CBT.

Same relation as above. Let x be the angle

Then:

so,

(iii) Consider the triangle ABD (or BCD).

Use the Pythagorean theorem (I'm the one who found it, I'm such a genious) to get DB:

or

i.e.

i.e.

(iv) Consider the triangle DBT.

Let

Then:

or

so

i.e.

That's it!

Just to have a little bit more confidence in our answer, and since the mast has a fixed height (12 m) you should notice that the longer the baseline is, the smaller should the angle be.

When the baseline is:

15 m (BC), the angle is

25.7 m (AB), the angle is

29.8 m (DB), the angle is

I hope these help.