please answer this trig question asap my homework is due today

Question

Question:

(please answer this question asap I really need help by today since my homework is due today and if possible can you provide the formula you used?)



Two walls of a canyon form the walls of a steady flowing river. From a point on the shorter wall, the angle of elevation to the top of the opposing wall is 20° and the angle of depression to the bottom of the opposing wall is 260 feet. Using the appropriate right triangle solving strategies, solve for the following: (Do not round intermediate calculated values. Only the final answer should be rounded to one decimal place.)

ibb.co/vvF1Hcy (picture/image)

the height of the short wall (x)

the height of the tall wall (y)

the distance between the canyon walls (z)

x = ___ feet

y = ___ feet

z = ___ feet

Provided image: ibb.co/vvF1Hcy 

Reason for asking: My reason for asking is because I have many questions like this on my homework sheet but the problem is I don't know how to answer them. I was/am hoping that someone would answer the question and go over the steps so that I can understand and try to use it in my other questions.

Due: Today

Thanks for the help.

Answer 1

Good idea to use SOHCHATOA! That's exactly what we need to do.

We know that each corner of the square is 90 degrees so the angle of elevation from the river to the 260 ft is 45 degrees. Now we have a 45-45-90 degree triangle that with sides of x, z and 260 feet.

we know sin(45) = opposite/hypotenuse and cos(45) = adjacent/hypotenuse.

Fun fact this means that opposite side = adjacent side because sin(45) = cos(45)

From the picture opposite = x and adjacent = z and hypotenuse = 260 ft and we can rewrite the equations as:

sin(45) = x/260

cos(45) = z/260

There from x = 183.85 and z = 183.85

For y its a bit tricky because we have 2 parts from the bottom triangle and the top triangle. so y = y1 + y2 but we know that y1 = x so we just need to find the height that is above that.

Here we have a 20-70-90 triangle that has a base equal to the width of the river (z) so we can use that with SOHCAHTOA where tan (20) = opposite/adjacent or tan (20) = y2/z

We found z (above) = 183.85

So plugging that in tan (20) = y2/(183.85) and y2 = 66.92

Answer 2

Looking at the picture

x / 260 = sin 45

z / 260 = sin 45

y = x + p where p / z = tan 20, so p = z tan 20

Answer 3

Hello San

Pl recheck this

"and the angle of depression to the bottom of the opposing wall is 260 feet. "

As angle can be in degrees and not in feet

I can answer all your questions after this small query