Pre-Cal: solve 45-deg triangle for r; find balloon hght; etc

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asimon2005

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I really need help for these problems. I just started Pre-cal and I'm a little scared and I already need help.

Here are the 5 problems 54-62 even I need help on. My Pre-Cal book is called Precalculus with Limits: A graping approach Fourth Edition by Larson, hosteltler, and edwards. It's on page 275-276 if someone has the same book as me and would like to help me. Thanks in advance.

In my book it says In Exercises 53-56, solve for x, y, or r, as indicated.
54. Its's a 45 degree triangle. The hypotenuse is r and the opposite is 20. It says solve for r.

56. It's a small 75 degrees triangle. It has r for the hypotenuse and the adjacent is 25. Solve for R.

58. Height: A 30-meter line is used to tether a helium-filled balloon. Because of a breeze, the line makes an angle of approximately 75 degrees with the ground.
(a) Draw a right triangle that gives a visual representation of the problem. Show the know quantities of the triangle and use a variable to indicate the height of the balloon.
(b) Use a trigonometric function to write an equation involving the unknown quantity.
(c) What is the height of the balloon?

60. Height of a Mountain: In traveling across flat land you notice a mountain directly in front of you. Its angle of elevation (to the peak) is 3.5 degrees. After you drive 13 miles closer to the mountain, the angle of elevation is 9 degrees. Approximate the height of the mountain.

62. Jin Mao Building: You are standing 65 meters from the base of the Jin Mao Building in Shanghai, China. you estimate that the angle of elevation to the top of the 88th floor(sightseeing level) is 80 degrees. What is the approximate height of the building? One of your friends is on the sightseeing level. What is the distance between you and your friend?

I need this by tomorrow morning.
 
>In my book it says In Exercises 53-56, solve for x, y, or r, as indicated.
54. Its's a 45 degree triangle. The hypotenuse is r and the opposite is 20. It says solve for r.

Since it has a hypotenuse it must be a right triangle. If one of the acute angles is 45° what is the measure of the other acute angle. If two angles in a triangle are equal, what can you say about the sides opposite these two equal angles. Since it is a right triangle, a fellow named Pythagorus had a theorem named after him that, if applied, gives your answer.

>56. It's a small 75 degrees triangle. It has r for the hypotenuse and the adjacent is 25. Solve for R.

I can only guess at what you are saying. I have to go to bed. I'm wondering why you waited until the last minute to do your homework. If that is the way you are going to approach this class, you will need much luck. In the future, please state your problem exactly as the book states it. Be complete. And show us what you have done so far so that we can possibly discover where you are going wrong.
 
Hello, Asimon,

I'm sure you already know how to do simple trig. Does (SOH -- CAH -- TOA ) sound familiar? That's what all these problems require.

Hint 1: Always draw a picture, and label every piece of info you know from the problem statement. The pics for these problems should all include right triangles.

Hint 2: Figure out which sides are Opposite, Adjacent, and Hypotenuse. Apply the formulas and you're done.

Hint 3: Show some work and you'll get LOTS more help from contributors on this site. :)
 
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