Alvin is 9 years younger than Elga. The sum of their ages is 67. What is Elga's age?
2 answers:
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Answer:
So 67 degrees is one value that we can take the sine of such that is equal to cos(23 degrees).
(There are more values since we can go around the circle from 67 degrees numerous times.)
Step-by-step explanation:
You can use a co-function identity.
The co-function of sine is cosine just like the co-function of cosine is sine.
Notice that cosine is co-(sine).
Anyways co-functions have this identity:
or
You can prove those drawing a right triangle.
I drew a triangle in my picture just so I can have something to reference proving both of the identities I just wrote:
The sum of the angles is 180.
So 90+x+(missing angle)=180.
Let's solve for the missing angle.
Subtract 90 on both sides:
x+(missing angle)=90
Subtract x on both sides:
(missing angle)=90-x.
So the missing angle has measurement (90-x).
So cos(90-x)=a/c
and sin(x)=a/c.
Since cos(90-x) and sin(x) have the same value of a/c, then one can conclude that cos(90-x)=sin(x).
We can do this also for cos(x) and sin(90-x).
cos(x)=b/c
sin(90-x)=b/c
This means sin(90-x)=cos(x).
So back to the problem:
cos(23)=sin(90-23)
cos(23)=sin(67)
So 67 degrees is one value that we can take the sine of such that is equal to cos(23 degrees).
The equation can be used to solve for the measure of angle abc is sinx = 2.4/10.3
<h3 /><h3>SOH CAH TOA identity</h3>The identity is used to find the measure of sides and acute angles of a right triangle
From the diagram shown, <ABC is the reference abgle hence;
Opposite side = 2,4cm
Hypotenuse .=10.3cm
According to the identity
sin x = opp/hyp
sinx = 2.4/10.3
sinx = 0.233
x = 13.47 degrees
Hence the equation can be used to solve for the measure of angle abc is sinx = 2.4/10.3
Learn more on SOH CAH TOA here: brainly.com/question/20734777
