LC trigonometry question

dodzy

Anyone point me in the right direction here for my daughter please

Looking for the height of the tree ! Thanks in advance.

ZorbaTehZ

Try and get a value for |AC| by considering the triangle ADC, then knowing |AC| you can get h by considering the triangle ACB.

EDIT: I've looked at the text at the top corner of the picture and it seems that this is a river, so it is not as I thought it was (next time please post the whole question). Anyways assuming that this is 3-dimensional (i.e. the tree is perpendicular to the plane through points A,C,D), and assuming that the sides of the river are parallel (presumably this is stated in the question, which cant be seen) then notice that DAC is a right-angled triangle - try and get an expression for AC and DC in terms of h and then combine these.

Michael Collins

ZorbaTehZ wrote: »

Try and get a value for |AC| by considering the triangle ADC, then knowing |AC| you can get h by considering the triangle ACB.

EDIT: I've looked at the text at the top corner of the picture and it seems that this is a river, so it is not as I thought it was (next time please post the whole question). Anyways assuming that this is 3-dimensional (i.e. the tree is perpendicular to the plane through points A,C,D), and assuming that the sides of the river are parallel (presumably this is stated in the question, which cant be seen) then notice that DAC is a right-angled triangle - try and get an expression for AC and DC in terms of h and then combine these.

Yep, this is the way to go with this one.

As a hint, from the triangle ABC, we know that |AC| = h tan(30 deg). See if you can verify this, and then try and find |DC| in terms of h as well (you will get this from the triangle DBC).

Now, consider the triangle ACD, you know two lengths, you know that it has one right angle, so apply a well-known theorem to find an equation in h, and solve for h.

The answer should come out to be [latex] h = 6\sqrt{6} [/latex]

dodzy

Thank you kindly lads. Apologies for omitting the question in the pic. I'll pass on the info. Again, much appreciated:)