Let's work on the left side first. And remember that
the<u> tangent</u> is the same as <u>sin/cos</u>.
sin(a) cos(a) tan(a)
Substitute for the tangent:
[ sin(a) cos(a) ] [ sin(a)/cos(a) ]
Cancel the cos(a) from the top and bottom, and you're left with
[ sin(a) ] . . . . . [ sin(a) ] which is [ <u>sin²(a)</u> ] That's the <u>left side</u>.
Now, work on the right side:
[ 1 - cos(a) ] [ 1 + cos(a) ]
Multiply that all out, using FOIL:
[ 1 + cos(a) - cos(a) - cos²(a) ]
= [ <u>1 - cos²(a)</u> ] That's the <u>right side</u>.
Do you remember that for any angle, sin²(b) + cos²(b) = 1 ?
Subtract cos²(b) from each side, and you have sin²(b) = 1 - cos²(b) for any angle.
So, on the <u>right side</u>, you could write [ <u>sin²(a)</u> ] .
Now look back about 9 lines, and compare that to the result we got for the <u>left side</u> .
They look quite similar. In fact, they're identical. And so the identity is proven.
Whew !
The similarity relationship is AC / EC = AB / ED.
The length of AB is 157.50m.
<h3>What is the length of AB?</h3>
When two triangles are similar, the ratio of the known sides of the triangles can be used to determine the length of the side of the unknown length.
The similarity relationship is : AC / EC = AB / ED
AC = 160 + 50 = 210
210 / 160 = AB / 120
AB = (210 X 120) / 160 = 157.50
To learn more about similar triangles, please check: brainly.com/question/10658464
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Answer:
1. The y-intercept 8 means you start off with $8. The slope 1/4 means how much money you have to pay for the amount of tickets purchased for carnival games.
2. The y-intercept 2 means the number of chapters you started reading and the slope 5/4 means the number of chapters you read per day.
3. The y-intercept 3 means the inital (start) cost of a muffin delivery and the slope 2 means the cost of each muffin delivery for the number of muffins you ordered.
Number 3 on the slope part might be the other way around if I'm wrong :)
Answer:
a 72
Step-by-step explanation:
9x10=90, so in total he has 90 pencils. if he loses 18 of them that's 90-18 which is 72.
The answer is D) because C) and B) are biased and would not be reasonable and A) has no guarantee of every third child being 12.
