### Video Transcript

π΄π΅πΆ is an isosceles triangle
where π΄π΅ is equal to π΄πΆ which is equal to 5.8 centimetres and angle π΅ is equal
to 48 degrees eight minutes and 32 seconds. Find the length of π΅πΆ giving the
answer to one decimal place.

Where possible, it is always useful
to draw a diagram. We were told that the triangle is
isosceles, and that length π΄π΅ was equal to length π΄πΆ. Both of these lengths were equal to
5.8 centimetres. We were also told the size of angle
π΅, 48 degrees eight minutes and 32 seconds. We need to convert this into just
degrees.

One degree is equal to 60
minutes. And one degree is also equal to
3600 seconds, as there are 60 seconds in a minute. And 60 multiplied by 60 is equal to
3600. We can, therefore, convert eight
minutes into degrees by dividing eight by 60. This is equal to 0.1333 and so on
degrees. We can convert 32 seconds into
degrees by dividing 32 by 3600. This is equal to 0.00888 and so on
degrees.

Adding these two numbers together
will give us a value in degrees of eight minutes and 32 seconds. This is equal to 0.1422 and so
on. We can, therefore, say that angle
π΅ is equal to 48.14 degrees to two decimal places. Where possible, we want to avoid
rounding our answers until the end to ensure that our final answer is as accurate as
possible.

Our next step is to split the
isosceles triangle π΄π΅πΆ into two right-angled triangles by drawing a vertical line
from the vertex π΄ to the line πΆπ΅. We will call the foot of this
vertical line π·. We have been asked to work out the
length of π΅πΆ. If we let the length of π·π΅ equal
π₯, then we know that π΅πΆ will be double this length, as the two right-angled
triangles are identical.

We can now use right angle
trigonometry, or SOHCAHTOA, to calculate the length π₯, which in turn will enable us
to calculate the length of π΅πΆ. If we consider the triangle π΄π΅π·,
the length π΄π΅ is the hypotenuse, as it is the longest side of the right-angled
triangle. The length π΄π· is the opposite, as
it is opposite the angle we are working with. Finally, the length π·π΅ labelled
π₯ is the adjacent, as it is adjacent, or next, to the 48.14-degree angle and the
right angle.

We know the length of the
hypotenuse. And weβre trying to calculate the
length of the adjacent. Therefore, we will use the cosine
ratio. This states that cos π is equal to
the adjacent divided by the hypotenuse. Substituting in our values gives us
cos of 48.4 is equal to π₯ divided by 5.8. We can multiply both sides of this
equation by 5.8. This gives us π₯ is equal to 5.8
multiplied by cos of 48.14. Typing this into the calculator
gives a value for π₯ equal to 3.8702 and so on.

As π₯ was the length π·π΅, then
π·π΅ is equal to 3.8702. We mentioned earlier that π΅πΆ is
double this length. Therefore, π΅πΆ is equal to 7.7404
and so on. We were asked to give our answer to
one decimal place. This means we need one number after
the decimal point in the answer. The four in the hundredths column
is the deciding number. As this is less than five, we will
round down. This means that the length of π΅πΆ
to one decimal place is 7.7 centimetres.