Trigonometry Problem Solving

[math_struggler]

There's a trig problem that I've hit a wall with. I am completely at a lost with where to even begin.

So, a bridge spans a river and the two identical sections of the bridge are each of length x metres. This bridge can be raised to allow tall boats to pass. When the two sections are fully raised, they are inclined at 70 degrees to the hoziontal and there is an 18 metre gap between them. Calculate the width of the river in metres.

I feel as though either the sine or the cosine rule is to be implemented but I'm not too sure on where to even begin.

Any help would be greatly appreciated. Attached is a quick diagram that I drew up.

 

[stapel]

A bridge spans a river and the two identical sections of the bridge are each of length x metres. This bridge can be raised to allow tall boats to pass. When the two sections are fully raised, they are inclined at 70 degrees to the hoziontal and there is an 18 metre gap between them. Calculate the width of the river in metres.
View attachment 4143

Thank you for the "sketch". Graphics can be very helpful! :cool:

To start, draw a "height" line from, say, the right-hand end of the "18m" section. This cuts off a right triangle. Label the base of just this triangle as "y". Then the cosine of the base angle has the value y/x. Create this equation.

The base of the trapezoid you've drawn is y + 18 + y = 18 + 2y. But the base, when the "arms" are folded back down (to create the bridge), is also x + x = 2x. This means that you have two ways of expressing the same length, which allows you to create a second equation.

You now have two equations in two unknowns, which you can solve.

 

[math_struggler]

Then the cosine of the base angle has the value y/x. Create this equation.

Sorry, but how would the base angle have the value of y/x? Could you please explain that a little bit more if at all possible?
Thanks so much for the help

 

[stapel]

Sorry, but how would the base angle have the value of y/x? Could you please explain that a little bit more if at all possible?

Draw the described triangle. Label the sides as described. Which sides then form the cosine ratio?

 

[math_struggler]

Which sides then form the cosine ratio?

Ohhh right, sorry that was a major mind blank
Soo cos70 = y/x right?

 

[stapel]

...the cosine of the base angle has the value y/x.

So cos70 = y/x right?

Yes, the cosine of the base angle, 70, has a value y/x.

 

[aleezasss]

the two equations y+9=x
u would sub into y+cos50x? they y just cancels out