Can someone help me with this trigonometry / algebra problem?

Question

Jungle Jim sees a signal on the top of an escarpment (a tall cliff) at an angle of elevation of 10 degrees. Later, after moving 1000 meters, the angle of elevation is 32.5 degrees. How tall is the escarpment?
I've tried to figure the question out a few ways with no luck. What would be the equation I would use with my scientific calculator??? This is the last question I have to do and have successfully done the rest on my own. Can anyone help?

Answer 1

Start by drawing a picture of this. Draw a right triangle. I put the right angle at the bottom left. Then draw an arbitrary line from the upper left vertex down to the base. This separtes the large right triangle into a smaller right triangle and what I will call the "outer triangle." This gives you the 1000 Jim moved; it's to the right of where the line intersects the base. I called this leg a. I drew in the angles I was given, and labeled all of the line segments. The hypotenuse of the large right triangle is b, the hypotenuse of the smaller right triangle (also the only unlabeled leg of the outer triangle) is c, and the vertical leg of the right triangle is d. d is the height of the escarpment. I named the angles after the sides they face. So the 10 degree angle is C, the 32.5 degree angle is D, and angle A is opposite leg a, and is an acute angle in the outer triangle. Since I was given angle D, I could find its supplement, B, which is an obtuse angle in the outer triangle, opposite leg b. B = 180 - D = 180 - 32.5 = 147.5. Since the sum of angles in a triangle is 180, and I know C and B, I can also find A = 180 - B - C = 180 - 147.5 - 10 = 22.5.

Now that I know every angle in the outer triangle and the length of one leg, a, I can use the law of sines. The law of sines says that a / sin(A) = b / sin(B). Rearranging, b = a*sin(B) / sin(A) = 1000*sin(147.5) / sin(22.5). Now look at the larger right triangle. You know the length of the hypotenuse, b, and you know the angle C opposite the unknown d (I called it C because it is also opposite leg c in the outer triangle.). By trigonometry, d = b*sin(C) = b*sin(10), where we use b from above.

Answer 2

Try this:

y = (1000 * sin 10 * sin 32.5)/(sin 10 - sin 32.5)

or

y = 1000/(csc 10 - csc 32.5)

any of the equation above will work for sure.

and their answer is 131.2348103 m

Answer 3

You must have found out this in algebra one million. It's simply asking you to uncover the slope then uncover the equation of the road. Remember slope is (y1-y2)/(x1-x2) so that is (five-one million)/(one million-three)=-two y=mx+b y=-2x+b Now you simply decide on a type of 2 elements they gave you and plug within the numbers to uncover b. I'll use (one million, five) however you get the equal reply for those who use (three, one million). five=-two(one million)+b five=-two+b b=7 So the equation is y=-2x+7 If you desire it within the sort of y+ax=c you simply rearrange it. y=-2x+7 y+2x=7