Find the value of each variable. Write your answer in radical form
2 answers:
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<u>Solution-</u>
As given in △ABC,
As from the properties of trigonometry we know that, the greater the angle is, the greater is the value of its sine. i.e
According to the sine law,
In order to make the ratio same, even though m∠A>m∠B>m∠C, a must be greater than b and b must be greater than c.
Also given that its perimeter is 30. Now we have to find out whose side length is 7. So we have 3 cases.
Case-1. Length of a is 7
As a must be the greatest, so b and c must be less than 7. Which leads to a condition where its perimeter won't be 30. As no 3 numbers less than 7 can add up to 30.
Case-2. Length of b is 7
As b is greater than c, so c must 6 or less than 6. But in this case the formation of triangle is impossible. Because the triangle inequality theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side. If b is 7 and c is 6, then a must be 17. So no 2 numbers below 7 can add up to 17.
Case-3. Length of c is 7
As this is the last case, this must be true.
Therefore, by taking the aid of process of elimination, we can deduce that side c may have length 7.
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Answer:
see below for instructions
Step-by-step explanation:
You will need to do these constructions yourself. We cannot put marks on your paper for you.
The instructions below apply to part 3. A subset of the instructions applies to parts 1 and 2. The tools you need are a compass and a straightedge.
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1. Draw line AB, and mark point X on it.
2. Choose a suitable radius for your compass and draw arcs with that radius centered at X. Label the points of intersection with line AB points E and G.
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From here, the instructions are the same for constructing a perpendicular bisector of any segment. In what follows, we are construction the perpendicular bisector of segment EG. Thus, these instructions apply directly to parts 1 and 2. Points E and G will refer to the end points of the segment you are bisecting.
3. Set your compass radius to <em>more than half the distance</em> between points E and G.
4. Draw an arc centered at E that extends above and below the center of segment EG.
5. <em>Using the same radius</em>, draw arcs centered at G that cross the arc you drew in step 4. Label the points of intersection point P and Q.
6. Draw line segment PQ. This is the perpendicular bisector of EG. (For part 3, it will go through point X.)
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In the attached, we show the "arcs" as full circles. They need not be. They only need to have sufficient length to make sure they cross where they need to cross.
