### Video Transcript

Four sketches of triangles are
shown. The longest side of each triangle
is one centimeter. The other length is given to two
decimal places. Part a) Circle the value of sin 35
degrees to two decimal places.

There is also a part b) to this
question which we will look at later. The sine ratio or sin 𝜃 is equal
to the opposite divided by the hypotenuse of a right-angled triangle. You might remember this from the
SOH part of SOH CAH TOA. Of the four triangles shown, only
two are right-angled. Therefore, we will focus on these
two triangles. The longest side opposite the right
angle is the hypotenuse. In both cases, this is equal to one
centimeter.

The 0.57 centimeters in the first
sketch is opposite the 35 degrees, whereas the 0.82 in the second sketch is next to
or adjacent to the 35 degrees. As the second triangle has the
adjacent and hypotenuse, this would enable us to calculate the cos or cosine of 35
degrees. Since we were asked to work out the
sine of 35 degrees, we’ll use the first triangle.

Substituting in the values from
this triangle gives us sin 35 is equal to 0.57 divided by one. Remember the opposite is the
numerator and the hypotenuse is the denominator. Any number divided by one is equal
to itself. Therefore, 0.57 divided by one is
equal to 0.57. We can therefore see that sin 35 is
equal to 0.57. The correct value correct to two
decimal places is 0.57.

The second part of the question
says the following. b) Calculate the value of 𝑧, giving your answer to one decimal
place.

As the triangle is right angled, we
can once again use SOH CAH TOA. Our first step is to label the
sides of the triangle. The seven centimeters is the
longest side and is opposite the right angle. Therefore, this is the
hypotenuse. 𝑧 is the opposite as it is
opposite the 35 degrees. Finally, the third side is the
adjacent as it is adjacent or next to the 35-degree angle and the right angle.

In this question, once again, we
want to use the sine ratio as we have the hypotenuse and want to calculate the
opposite. As mentioned in part a), sin 𝜃 is
equal to the opposite divided by the hypotenuse. Substituting in our values gives us
sin 35 is equal to 𝑧 divided by seven. Multiplying both sides of this
equation by seven gives us seven multiplied by sin 35 is equal to 𝑧. In part a) of the question we
established that sin 35 was equal to 0.57 to two decimal places. This means that 𝑧 is equal to
seven multiplied by 0.57.

There are lots of ways of working
out this answer. One way would be using the
traditional column method: 0.57 multiplied by seven. Seven multiplied by seven is equal
to 49. So we put a nine in the hundreds
column and carry the four. Seven multiplied by five is equal
to 35. Adding the four gives us 39. We put a nine in the tenths column
and carry the three. At this point, remember to include
the decimal point in the correct place. Seven multiplied by zero is equal
to zero. Adding three to this gives us
three. Therefore, 0.57 multiplied by seven
is equal to 3.99. We can therefore say that the
length 𝑧 in the right-angled triangle is 3.99 centimeters.

An alternative method for
multiplying seven by 0.57 would be to multiply 0.5 by seven and then 0.07 by
seven. 0.5 multiplied by seven is equal to
3.5 or 3.50. If we think of this in money terms,
seven lots of 50 pence is three pound 50. In the same way, 0.07 multiplied by
seven is equal to 0.49. Once again, seven lots of seven
pence is equal to 49 pence. Adding these two values 3.50 and
0.49 once again gives us 3.99.

In this question, we were asked to
give our final answer to one decimal place. This means that we only want one
number after the decimal point. The second nine is the deciding
number. And as this is greater than five,
we’ll round up. This means that the value to one
decimal place is 4.0 or just four centimeters.