First we need to see in which quadrant 11pi/6 lies And it lies in fourth quadrant. And to find the reference angle in the fourth quadrant, we need to subtract the given angle from 2 pi . For e.g if the angle is 5pi/3, then the reference angle is 2pi - (5pi/3) = pi/3 .
So for the given question, reference angle of 11pi/6 is
And that's the required reference angle .
Since BC is the hypotenuse...
α = 12
c = 13
Hence..
13² = 12² + ß²
ß = √(13² - 12²)
= √(169 - 144)
= √25
= 5
Hence, AB = 5
I hope this helps!
Something that a right triangle is characterised by is the fact that we may use Pythagoras' theorem to find the length of any one of its sides, given that we know the length of the other two sides. Here, we know the length of the hypotenuse and one other side, therefor we can easily use the theorem to solve for the remaining side.
Now, Pythagoras' Theorem is defined as follows:
c^2 = a^2 + b^2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.
Given that we know that c = 24 and a = 8, we can find b by substituting c and a into the formula we defined above:
c^2 = a^2 + b^2
24^2 = 8^2 + b^2 (Substitute c = 24 and a = 8)
b^2 = 24^2 - 8^2 (Subtract 8^2 from both sides)
b = √(24^2 - 8^2) (Take the square root of both sides)
b = √512 (Evaluate 24^2 - 8^2)
b = 16√2 (Simplify √512)
= 22.627 (to three decimal places)
I wasn't sure about whether by 'approximate length' you meant for the length to be rounded to a certain number of decimal places or whether you were meant to do more of an estimate based on your knowledge of surds and powers. If you need any more clarification however don't hesitate to comment below.
Find the lengths of the sides. Determine how long a right triangle side lengths are.
