Ahh okay last question. Convert to degrees.?

Question

http://online.math.uh.edu/webct/fall06/1330/q9/images/q9_problem15__55.gif

I am usually good at this, but wow...I do not what to do. I need exact answers please. Steps would be really helpful.

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A wire is to be stretched from the top of a 9 meter-high building to a point on the ground. The angle that the wire makes with the ground is 25o. How long is the wire (in meters)?


I also had this problem. Well, I got x = 9/sin(25). Sadly that was not an answer. Here are the answers:

1. 9/cos(115)

2. 9/tan(25)

3. 9/cos(25)

4. 9/sin(25)

5. 9/cos(65) < ---- could this possibly be it. (draw a diagram, it works)

6. NONE OF THE ABOVE.

Answer 1

C = 9/sin 25 (I use C because it denotes hypotenuse) is indeed the correct answer, and here is why, but it is also equivlanet to C = 9/cos65

We know that the height of the building is 9 meters, so H = 9 meters

We also know that the angle the wire makes with the ground is 25 degrees.

What we are looking for is the length of this wire, which is really the hypotenuse of this triangle (your diagram should be a triangle).

H is the length of the triangle that is opposite to the known angle, and we are solving for the hypotenuse, so let’s use sin 25 = 9/ C

C = 9 / sin 25, which is approximately 21.30 meters.

So that answer is indeed correct, but there is another way of saying the same thing. Since the degree by the ground is 25, we know the other degree must be 65 because the two must add up to 90. We also know that the sin of one of them is equivalent to the cosine of the other, so the sin of 25 degrees is the same as cosine of 65 degrees. Thus, the 9/sin25 is equivalent to 9/cos65, so that is the correct answer in this case.

Now for the conversion of degrees. It is important to remember the formula for converting from degrees to radians: 1 radian = 180/pi degrees.

So first we have: 7/10 * 180/pi

which is 1260/10pi

This reduces to 126/pi, so your answer in exact form, in terms of pi, is 126/pi.

For 1/pi, we have: 1/pi * 180/pi

Which gives us 180/pi^2

(180 divided by pi squared)

Answer 2

Make a quick sketch of a right angled triangle ABC as follows:-
Right angle is B
Vertical is AB = 9
Hypotenuse AC = h
Angle ACB = 25°
sin 25° = 9 / h
h.sin 25° = 9
h = 9 / sin 25°-----ANSWER 4.