bearing problems (navigation)

It's my finals tomorrow in Trigonometry and I need to pass. Most of the questions are from the topic bearing. Here are some of the questions that my professor always give. Can you please help me answer these? I also like to have the sketch of this.

1. Two observers A and B are on the opposite sides of the tower 115 m high. From observers, A and B, the angle of elevation to the top of the tower is 57 degrees 17 minutes and 13 degrees 25 minutes, respectively. Find the distance between the 2 observers.

2. A hiker walks 1.5 km on a bearing of 35 degrees. At this point he turns directly south and walks 3.5 km. How far and on what bearing must he walk to return to his original position?

Re: bearing problems (navigation)

1.) You will have right triangles on opposite sides of the tower. You are trying to find the sides adjacent to the given angles, and you know the side opposite the angle is the height of the tower. What trig. function relates an angle to the opposite and adjacent sides?

Re: bearing problems (navigation)

Quote:

Originally Posted by

**MarkFL2** 1.) You will have right triangles on opposite sides of the tower. You are trying to find the sides adjacent to the given angles, and you know the side opposite the angle is the height of the tower. What trig. function relates an angle to the opposite and adjacent sides?

tangent

Re: bearing problems (navigation)

Yes, so let *a* be the distance that A is from the tower and *b* be the distance that B is from the tower. Can you state *a* and *b* in terms of the given angles using the tangent function?

Re: bearing problems (navigation)

Quote:

Originally Posted by

**MarkFL2** Yes, so let *a* be the distance that A is from the tower and *b* be the distance that B is from the tower. Can you state *a* and *b* in terms of the given angles using the tangent function?

tan 57deg17min = 115m/a

tan 13deg25min = 115m/b

Re: bearing problems (navigation)

Yes, but you want to solve these for *a* and *b* respectively. Then $\displaystyle a+b$ is the distance between the two observers. To evaluate the tan function, you need to convert the given angles to degrees, make sure your calculator is in degree mode, and then plug in the angles.

Re: bearing problems (navigation)

Quote:

Originally Posted by

**MarkFL2** Yes, but you want to solve these for *a* and *b* respectively. Then $\displaystyle a+b$ is the distance between the two observers. To evaluate the tan function, you need to convert the given angles to degrees, make sure your calculator is in degree mode, and then plug in the angles.

my answer is 555.9733066 = 555.97 m

Re: bearing problems (navigation)

Yes, I agree with that result.

For the second problem, draw a sketch and you will find you have two known sides of a triangle and the angle subtending them. Is there a "law" that relates the unknown side to these known values?