PROBLEM #1: Find the lengths of PR and QS.

Mathematics

1 answer:

egoroff_w [7]3 years ago

3 0

Answer: PR= 20

QS=20

Step-by-step explanation:

The triangles are both congruent and isosceles. 10 + 10 = 20

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zepelin [54]

You can make some algebraic equations and solve it.
The first would be:
$x \times y = - 21$
The second would be
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You can then rearrange the second into
$x = - 4 - y$
And subsitute it into the first like so:
$( - y - 4) \times y = - 21$
After that, distribute the y into the parantheses.
${ - y}^{2} - 4y = - 21$
Subtract the 21 on both sides and multiply by -1 on both sides:
${ - y}^{2} - 4y + 21 \\ {y}^{2} + 4y - 21$
You then can factor it into:
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With Zero Product Property, we can determine y to be either -3 and 7. Since the variables are interchangable, you can say the same about x, just that whatever x is, y must be the other value.

Thus, the answer is 7 and -3.

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The definition of the tangent function tells you
tan(angle) = (300 ft) / (distance to mountain)
This equation can be rearranged to
(distance to mountain) = (300 ft) / tan(angle)

For the far end of the river,
distance to far end = (300 ft) / tan(24°) ≈ 673.8 ft

For the near end of the river
distance to near end = (300 ft) / tan(40°) ≈ 357.5 ft

Then the width of the river can be calculated by finding the difference of these distances:
width of river = distance to far end - distance to near end
width of river = 673.8 ft - 357.5 ft
width of river = 316.3 ft

The appropriate answer choice is
316 ft.

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