Question 480045: PQRS is a rectangle in which PQ=9 cm and PS=6cm.T is a point on PQ such that PT=7cm and RV is a perpendicular from R to ST . Calculate ST and RV?
Answer by cleomenius(959)   (Show Source):
You can put this solution on YOUR website! First, I made a triangle with the sides PS = 6cm and PT = 7 cm.
PSQ is a right traingle, as the angle SPQ is the corner of a rectangle.
This is in the left upper corner of the rectangle, and we find the hypotenuse, ST by 6^2 + 7^2 = x^2.
This works out to 9.2 cm, the size of ST, the first segment we are looking for.
With this we can find the angle PST with the sine function. sin 7/9.2 = 7.60, 49.5 degrees.
We now need to find RV which is one of the legs on triangle SVR.
We can find angle VSR, since we know PSV to be 49.5, and we know angle PSR is 90 degrees, as it is a corner in a rectangle.
So, 90 - 49.5 = 40.5, the measure of angle VSR.
Again, we can use the sine function, sine of 40.5 = opp/hyp = x/9.
0.649 * 9 = 5.85 cm. This is the size of RV.
Cleomenius.
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