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4 years ago

How you know when there is only one solution triangle possible from a side-side-angle?

Mathematics

1 answer:

erastova [34]4 years ago

5 0

Answer:

There will be only on solution if either of these conditions is met:

the given angle is opposite the longest side
the triangle is a right triangle (the ratio of the side opposite the angle to the other given side is equal to the sine of the angle)

Step-by-step explanation:

Consider the SSA geometry with the angle placed in standard position at the origin and its adjacent given side (the second side of SSA) extending along the +x axis. Draw a circle having a radius equal to the length of the first side of SSA, centered on the vertex between the two segments on the +x axis.

There are three possibilities for the way this circle intersects the other ray of the angle (the ray that is not the x-axis):

the first side is as long or longer than the second side, so there is one point of intersection (one solution to the triangle, purple in the attachment)
the first side is just long enough to be tangent to the other ray, so there is one point of intersection (one solution to the triangle, green in the attachment)
the first side is between these lengths, so intersects the other ray in two places, giving two solutions to the triangle, red in the attachment.

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3 years ago

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Devon needs a wood board with an area of 516 square yard to complete a project. If the wood board is 13 yard wide, how long must

nataly862011 [7]

Answer:

$L=\frac{15}{16}\ yd$

Step-by-step explanation:

The correct question is

Devon needs a wood board with an area of 5/16 square yard to complete a project. If the wood board is 1/3 yard wide, how long must the board be?

we know that

The area of a rectangle is equal to

$A=LW$

where

L is the length

W is the width

we have

$A=\frac{5}{16}\ yd^2\\\\W=\frac{1}{3}\ yd$

substitute

$\frac{5}{16}=L(\frac{1}{3})$

solve for L

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$L=\frac{15}{16}\ yd$

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3 years ago

Find the formula for the nth term of the sequence: 0,7,18,33,52

defon

Answer:

t(n) = 2n² + n - 3

Step-by-step explanation:

Given sequence:

0, 7, 18, 33, 52

Find the formula for nth term t(n)

<h3>Solution</h3>

Sequence is neither arithmetic nor geometric, analyzing:

0, 7, 18, 33, 52

First level difference

7, 11, 15, 19

Second level difference

4, 4, 4

As there are two levels, the formula should be in the form of:

t(n) = an² + bn + c

Trying the formula with the known terms:

t(1) = 0 ⇒ a+b + c= 0

t(2) = 4a + 2b + c = 7 ⇒ 3a + b = 7

t(3) = 9a + 3b + c = 18 ⇒ 3(3a+b) + c = 18 ⇒ 21 + c = 18 ⇒ c = -3

Going back to previous equations to find remaining coefficients:

t(1) ⇒ a+ b = 3 ⇒ t(2) = 2a + (a+b) = 7 ⇒2a + 3 = 7 ⇒ a= 2 ⇒ b = 1

So the formula becomes:

t(n) = 2n² + n - 3

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