Did you know that trigonometry can be used to calculate the position from the shore to a ship?
The person on the shore can find the angle between the shore and the ship and the ship's captain can find the angle from the ship to shore. It looks a bit like a pirate ship, so best we can locate their exact position in case we need help!
The sine rule is used to calculate angles in a non-right angled triangle. The formula is:
It looks the same as the sine rule for finding a side length. The difference is that the terms have been turned upside down with the angles (sin) being on the top.
You will need a scientific calculator in order to get the sin-1 button. Make sure it is set to degrees.
Calculate angle x.
Step 1: Label the angles of the triangle if it hasn't already been labelled. Our angles are A, B, and C. You are free to pick the order they go in.
Step 2: Label the lengths. This is where you have to be very precise, otherwise the formula will not work. The length opposite angle A must be called a, the length opposite angle B must be called b, and the length opposite angle C must be called c.
A = 60°
B = x
C = (blank)
a = 7cm
b = 6cm
c = (blank)
Step 3: Write the formula that you will need. Notice that length c and angle C are both blank, so in this case, we can leave them out:
sin A / a = sin B / b
Step 4: Substitute your known values:
sin 60 / 7 = sin x / 6
Step 5: Rearrange the formula to make sin x the subject:
sin x = 6 x (sin 60 / 7)
sin x = 0.74 ...
Step 6: Use inverse sin ("sin-1") to find the angle. (Just remember to press "shift" + "sin" on your calculator to make it appear).
x = sin-1 (0.74...)
x = 47.9° (to 3 significant figures)
NOTE: If you try to put it all into the calculator at once, the rules of BIDMAS aren't followed and your answer will be incorrect.
Let's give it a try...