# Thread: Some trig problems, fast help would be great!

1. ## Some trig problems, fast help would be great!

Hi everyone. Can someone please explain these questions?

1) Find the exact value of cos 105 degrees

how would i go about doing that? it's not just a simple calculator problem, but rather one probably involving 30-60-90 or 45-45-90 triangles. the answer has radicals in it.

2) A surveyor determines that the angle of elevation of a mountain peak is 35 degrees. Moving 1000 feet further away from the mountain, the surveyor determines the angle of elevation to be 30 degrees. Find the mountain's height.

Thanks!

2. Originally Posted by gobbajeezalus
Hi everyone. Can someone please explain these questions?

1) Find the exact value of cos 105 degrees

how would i go about doing that? it's not just a simple calculator problem, but rather one probably involving 30-60-90 or 45-45-90 triangles. the answer has radicals in it.
Hint: cos(105) = cos(60 + 45). now use the addition formula for cosine and continue

2) A surveyor determines that the angle of elevation of a mountain peak is 35 degrees. Moving 1000 feet further away from the mountain, the surveyor determines the angle of elevation to be 30 degrees. Find the mountain's height.

Thanks!
did you draw a diagram? if not, do so. you will realize the following:

Let the height of the mountain be $y$
Let the first position of the surveyor be $x$ feet from the mountain. then

$\tan 35^o = \frac yx$

$\tan 30^o = \frac y{x + 1000}$

you have two simultaneous equations with two unknowns, you are required to solve for one of them, namely $y$

3. PERFECT! #1 works like a charm.

as far as #2 goes, i'm not really sure how to proceed. i got it up to the diagram part, and i completely understand the equations provided, but how do i set them equal to each other?

thanks

4. Originally Posted by gobbajeezalus
PERFECT! #1 works like a charm.

as far as #2 goes, i'm not really sure how to proceed. i got it up to the diagram part, and i completely understand the equations provided, but how do i set them equal to each other?

thanks
one way: solve for x inthe first equation and plug it into the second. you will then have an equation where only y is unknown, you can solve for it