The value of 
for the angles 
and 
in standard position in the first quadrant is 
We need to find the value of . To proceed, we need to use the compound angle formula
<h3>
Cosine of a sum of two angles</h3>
The cosine of the sum of two angles and is given below
We are given
We need to find 
and 
, using the identity
<h3>Find sin(b)</h3>
To find , note that
substituting 
for 
in the identity, we get
<h3>Find cos(a)</h3>
To find , note that
substituting 
for 
in the identity, we get
<h3>Find the value of cos(a+b)</h3>
We can now make use of the formula
to find .
Learn more about sine and cosine of compound angles here brainly.com/question/24305408
Considering the area of the rectangle, we have that the length is of 8 units and the width is of 10 units.
<h3>What is the area of a rectangle?</h3>
The area of a rectangle of length l and width w is given as follows:
A = lw.
In this problem, the area is of 80 square units, while the length and the width are consecutive even integers, hence:
Then:
l(l + 2) = 80
l² + 2l - 80 = 0
(l + 10)(l - 8) = 0.
We need the positive measure, hence:
l - 8= 0 -> l = 8 units.
w = l + 2 = 10 units.
More can be learned about the area of a rectangle at brainly.com/question/10489198
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Let n be the common factor for the ratio 6:5. Then:
6n+5n=330
11n=330
n=30
aerobics=6n=180 min
weight training=5n=150 min
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