# Math Help - using sin & cos rules help please

1. ## using sin & cos rules help please

I have this q, i have drawn the diagram for it but am unsure to how to sove it...
A tower 60m heigh stands on top of a hill. from a point on the ground at sea level, the angles of elevation of the top & bottom of the tower are 49degree and 37degree respectively. find the height of the hill.

I tried the hyp x =60/12 for the angles and found this for the height and tower but took 60 of for the tower, but i dont understand what i did ,but i also got the wrong answer

Thank you

2. You will have two formulas.Notice that you have to add the height of the hill (x) to 60 in order to use 49 degrees as your angle. For your equation with 37 degrees as your angle, your opposite side will just be x.

Use tangent so that you are using a common adjacent side:

$\tan 49 = \frac {60+x}{adjacent}
$

and:

$\tan 37 = \frac {x}{adjacent}$

Isolate $adjacent$ in the second equation:

$adjacent = \frac {x}{\tan 37}$

Sub it into the first equation:

$\tan 49 = \frac {60+x}{\frac {x}{\tan 37}}$

Now solve for $x$ !

3. Just wondered if you couls explain this a little bit more please, as i dont fully understand where you have got the tan eqn from. Also i dont know where to go with finding x.....thank you

4. To solve a question like this what you need is common sides. I created two equations that have sides in common in order to solve for x.

To create my first equation, I knew that I wanted the distance from the point on the ground at sea level to the base of the hill to be in both equations because it would be the same in both. I also knew that I wanted to involve x in both equations somehow. I know that tangent is equal to opposite over adjacent, and that the angle 49 is to the top of the tower, and from this I derived:

$\tan 49 = \frac {60+x}{adjacent}$

My second equation was only to the top of the hill, and only 37 degrees so I derived this formula:

$\tan 37 = \frac {x}{adjacent}$

Then I simply isolated the adjacent side(as it is unknown) in one of my equations and plugged it into the other in order to solve for x.

To solve for x, multiply both sides by $\frac {x}{\tan 37}$ and then it will be easy.