Just a few ?? please help me

[Hot*Mamma]

1. 2 hikers are walking along a straight road. A straight path heads off at an angle of 47*(degrees) with the road. One hiker follows this path. The other hiker continues on the roadfor 52 m until he comes to a second straight path which goes off on the same side of the road as the first path. He travels 75 m along this path and meets the first hiker. What angle do the two paths makewith eachother? Round your answer to one decimal place.

2. A ship sails due north for 15km. It then tyurns east at an angle of 40* from north ans ssails another 7km. How far is it from its starting point? Give your answer to one decimal place. Give a diagram.

3. In triangle XYZ, XY=6 cm, YZ= 7cm, <Y = 78*. Find the length of XZ and the measure of <X. Give your answer to one decimal place.

 

[Unco]

Take the advice of (2.) and draw some diagrams.

The first one looks like

                                     *
                                 *  /
2nd hiker _                  * \_ /
          /|       75    *angle /
                     *        /
                 *          /
             *            /
         *              /
 /|\     |            /    _   1st hiker
  |      |          /      /|
  |   52 | 47deg  /      /
         | __   /      /  
         |/  \/       
         |  /  
         |/

The Law of Sines will be handy.

 

[soroban]

Hello, Hot*Mamma!

2. A ship sails due north for 15km.
It then turns east at an angle of 40° from north and sails another 7km.
How far is it from its starting point? Give your answer to one decimal place.
Give a diagram. . . . . good advice!

    N                C
    |               *
    |            *
    |       7 *   *
    |40°  *
    |  *        *
  B * 140°
    |         *
    |
    |       * b
  15|
    |     *
    |
    |   *
    |
    | *
    |
    *
    A

The ship starts at A, sailes 15 km north to B, turns 40° and sails 7 km to C.

Since \(\displaystyle \angle NBC\,=\,40^o,\:\angle CBA\,=\,140^o\)

We have \(\displaystyle \Delta ABC\) with: \(\displaystyle \,B\,=\,140^o,\:a\,=\,7,\:c\,=\,15\)

Use a Law of Cosines: \(\displaystyle \:b^2\:=\:a^2\,+\,c^2\,-\,2ac\cdot\cos B\)

 

[soroban]

Hello again, Hot*Mamma!

3. In triangle XYZ, XY=6 cm, YZ= 7cm, /Y = 78°.
Find the length of XZ and the measure of /X.
Give your answer to one decimal place.

Did you make a sketch?

You have two sides and the included angle.
\(\displaystyle \;\;\)Use the Law of Cosines to find the third side.

Once you know the three sides,
\(\displaystyle \;\;\)use the Law of Cosines to find any of the angles.