Stuck On Maths Question

robert12345

Hey, can anyone do Text And Tests 4 Chapter 2F Question 9? I've been looking at it for a while and can't seem to solve it.


Here is the question (I can't add the picture though!):
A river flows due east and a tower [cd] stands on its left-hand bank. From a point a up stream and on the same bank as the tower, the angle of elevation of the top of the tower is 60°. From a point b at right angles across from a, the angle of elevation is 45°. If the height of the tower is 36 metres, find the width of the river, correct to the nearest metre.

It looks close to something like this:

Laphroaig52

Use Tan 60 to calculate |ad|
Use Tan 45 to calculate |bd|

Armed with that knowledge, your old friend Pythagoras will help you to calculate |ab|

robert12345

I've tried that and got 41.5m but in the back of the book it says it's 29m.

Laphroaig52

robert12345 wrote: »

I've tried that and got 41.5m but in the back of the book it says it's 29m.

Try again.

The book never lies....

Laphroaig52

Flyer28 wrote: »

Try again.

The book never lies....

Hint: Be sure to apply Pythagoras correctly...

robert12345

Ok, here are the steps I've taken.

1) 36 ÷ Tan 60 = 12√3 = 20.78

2) 12√3 x Tan 60 = 12√3

robert12345

Also I did it the other way where I found the length of bd and divided it by 2 to get 29m which is the right answer but I don't understand why.

robert12345

Thanks for the help guys. I just find it really stupid how half the length from the point of the top of the tower to the point on the other side of the river is its length. It didn't give any indication wich point was the river length.

Laphroaig52

robert12345 wrote: »

Ok, here are the steps I've taken.

1) 36 ÷ Tan 60 = 12√3 = 20.78

2) 12√3 x Tan 60 = 12√3

Step 1 above gives you the correct solution for |ad|.

I'm not really sure what you are trying to do in Step 2!
But referring to arodabomb's reply, we know that |bd| = 36.

So now just apply Pythagoras to the triangle abd to solve |ab|.

In applying Pythagoras, note that |bd| is the hypotenuse!
This is where I think arodabomb went wrong also.

robert12345

Ok, thank you. The message I sent before is wrong.

robert12345

Last question, the only other one I couldn't solve on this chapter is question 11.

Question:
A vertical flagpole stands on horizontal ground. The angle of elevation of the top of the pole from a certain point on the ground is Θ (Theta). From a point on the ground 10 metres closer to the pole the angle of elevation is β (Beta). Show that the height of the pole is:

10sinΘsinβ

---

sin(β-Θ)

finality

robert12345 wrote: »

Last question, the only other one I couldn't solve on this chapter is question 11.

Question:
A vertical flagpole stands on horizontal ground. The angle of elevation of the top of the pole from a certain point on the ground is Θ (Theta). From a point on the ground 10 metres closer to the pole the angle of elevation is β (Beta). Show that the height of the pole is:

10sinΘsinβ

---

sin(β-Θ)

Here's a solution



sorry it's a bit blurry, the angle next to beta is (180 - beta)

basically you need the angle (beta - theta) so you realise that you can find that within the triangle on the left. It's a bit tricky to see what you need to do, I'd generally just mess around with it and try different things until the correct method jumps out at me. So if you don't know where to start, just try and find as many angles/sides as you can and eventually it should work out.

I'm just glad I can remember how to do maths since the leaving cert :L