Question

(PLEASE HELP!) A car travels 76 km due north and then 25 km due east.

(a) What is the cars current bearing from the starting point correct to the nearest degree?
(b) How far is the car from the starting point correct to the nearest km?​

Answer 1

Explanation:

Look at the File I attached. The Question says that a car travels 76 km north then 25 km east. Now think of this as the Right angled triangle I attached in the file.

a) Bearing from the staring point to the means the degrees of the part i marked with a question mark.

Now SOH CAH TOA

76 km is the ADJACENT

25 km is the OPPOSITE

and x is the HYPOTENUSE

We have the values of the ADJACENT and the OPPOSITE.

Now see which rule has both, It is TOA(tan rule) which is:

tan(y) = OPPOSITE/ADJACENT (y is the degrees we will get)

tan(y) = 25/76 ( opposite of the degree we need is 25 and adjacent is 76)

tan inverse(25/76) = y (inverse will be given as to the power -1 on the calculator)

FINAL ANSWER OF (a) = 18.21°

b) This part is asking for the length of the hypotenuse, which i denoted as x in the attached file.

For this part, you will use the Pythagoras Theorem

Which is :

a² + b² = c²

Where c is the hypotenuse and a and b are the opposite and adjacent.

So

76² + 25² = x²

6401 = x²

√6401 = x

x = 80.01