Having trouble with this maths question, can anyone help?

Question

I'm on the last question of my assignment, and I'm stuck. It's about trigonometry. The question is a bit lengthy to explain here, so I scanned it and uploaded it:

http://img147.imageshack.us/my.php?image=mathspage3zc3.jpg

It has a diagram and all the info you need.

Should I assume that the cliff meets the ground at 90 degrees? Or is there a way to do this that I am missing? The page does say to use the sine rule, but it looks like I don't have enough info to use it.

If someone could post the working out, the answer, or anything that could help me, I'd really appreciate it.

Thanks!

Answer 1

I'd assume the cliff meets the ground at a 90 degree angle.  Just try to get the measurements of each side of the triangles by using trigonometry methods.  Good luck.

Answer 2

I would also assume they're both 90 degree triangles. It doesn't say anything about Sine LAW, etc. So if you're told to use Sin, I would assume the Sin = Opposite/Hypoteneuse.

Answer 3

Yes, we'll assume the cliff is perpendicular to the ground.

Now, mark your angles in. From the breakdown to the top has an angle of 2.5° and from the rest point to the top has an angle of 4.25°.

Also, we know the distance between these two points is 5km and because he walked there in 1.5 hours, he would have to had walked at a speed of (3 + 1/3) km/h - 5 ÷ 1.5.

Now, remembering that there are 180° in a straight line - the angle opposite from the 4.25° would be 180 - 4.25 = 175.75°. Now also, there are 180° in a triangle and you'll notice that there is a triangle on the left so that means the angle between breakdown and the rest point to the top is 1.75°. Now, let the distance between the rest points and the top of the cliff be x. Using the sine rule:

(sin 25 / x) = (sin 1.75 / 5)

x = 5sin 25 / sin 1.75

x = 69.19 km

Now that we have x, we can use basic trigonometry to find the height of the cliff AND the distance from the rest point to the garage. Let the cliff height be t and let the distance from the rest point to the garage be y:

sin 4.25 = t / 69.19

t = sin 4.25 * 69.19

t = 5.13 km

The cliff height is 5.13 km.

Can you do the rest? I'm not going to do your whole assignment for you (that'd be cheating :P)

Answer 4

serious  dude. this is easy stuff. just find the length of both triangles.