Question

In a right angled triangle one of the angles is 45°. What is the third
angle? If the side adjacent to the 45° angle is 100 mm, find the lengths
of the other two sides.

I understand the first half of this question, I just dont know how to do the second half, any help of the easiest way to do this would be so much appreciated!

Answer 1

Did you try to Sin ?!

Answer 2

How much is the 45 dragee sin ?

Answer 3

First question
since it is a right triangle there should be an automatic 90 degrees angle given. Since you are given another angle which is 45 degrees you can find the other angle by equating all three angles to 180 degrees.
So it becomes 180 degrees=45degrees+90degrees+theta
giving you theta =45 degrees

Answer 4

Second Question

as shown in the figure you can see what the adjacent side means.
In order to get the length of the two sides you can use the sine,cosine and tangent.
Sine theta=opposite side/hypotenuse => opposite side meaning the side opposite the angle
Cosine theta=adjacent side/hypotenuse
tangent theta=opposite side/adjacent side

computing
tangent 45 degrees= opposite side/100mm
opposite side=100mm * tangent 45 degrees
opposite side=100mm*1
opposite side = 100mm

to compute for the hypotenuse you can use the cosine theta=adjacent side/hypotenuse
but you can also use the Pythagorean theorem which is
\[a ^{2}+b ^{2}=c ^{2}\]
where in a and b are the other two side of the triangle
and c is the hypotenuse
since we already computed for the other side we can use these theorem to compute for the hypotenuse

\[c ^{2}=100^{2}+100^{2}\]
giving you
\[c=100\sqrt{2}mm\]

Answer 5

@lisamc91 :)

Answer 6

@lisamc91 remember than tangent 45 degrees = 1 just try to memorize angles that are frequently use in sine cosine and tangent which are 30 45 60 and their corresponding values when you use them with sine.
For example sine 30 degrees= 1/2. Try to memorize those because they will come in handy for sure :)

Answer 7

oh thank you so much! thats great! @yeyenunez

Answer 8

you're welcome :)