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How do i solve this question? If Jay (PQ) is 3' 9" (or 45" inches) tall, how tall is...

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tjjavid | Student, Undergraduate | (Level 1) Honors

Posted May 15, 2013 at 8:54 PM via web

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How do i solve this question?

If Jay (PQ) is 3' 9" (or 45" inches) tall, how tall is his dad (P'Q')

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crmhaske | College Teacher | (Level 3) Associate Educator

Posted May 16, 2013 at 12:00 AM (Answer #1)

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First we have to solve for the angle PCQ'.  To do so we can use the trigonometric function sine:

`sintheta=(opp.)/(hyp.)=45/75->theta=36.9`

Next, using the same trigonometric function, we can solve for Jay's father's height (h)

`sin36.9=h/(75+50)->h=125sin36.9=75`

Therefore, Jay's father is 75'' in height, or 6'3''

Another method of solving this problem is using the knowledge that the ratios between each person's height and the hypotenuse are equal to each other because the angle is the same, therefore:

`45/75=h/125-gth=(125)(45)/75=75`

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