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tiny-mole [99]
3 years ago
11

7) Line Segment PR is 5 ft. Find the length of Line Segment PQ and QR. (Hint: use the segment addition postulate.)

Mathematics
1 answer:
Ghella [55]3 years ago
4 0

Answer:

PQ = 1 ft

QR = 4 ft

Step-by-step explanation:

From the picture attached,

Segment PR has been divided into two parts by a point Q.

Length of segment PR = 5 feet

Length of segment PQ = (15x - 2) ft

Length of segment QR = (5x + 3) ft

Since, PR = PQ + QR

5 = (15x - 2) + (5x + 3)

5 = 20x + 1

20x = 4

x = \frac{4}{20}

x = 0.2

PQ = 15x - 2

     = 15(0.2) - 2

     = 3 - 2

     = 1 ft

QR = 5x + 3

     = 5(0.2) + 3

     = 1 + 3

     = 4 ft

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Tan A = 1/2 means that the right triangle containing angle A has legs of length 1 and 2 units. So the hypotenuse  = √(1^2 + 2^2) = √5  (using the Pythagoras theorem). The side opposite to < A = 1 unit and the adjacent side = 2 (as tan = opposite / adjacent).

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cos A / sin A = 2/√5 /  1/ √5 =  2.

sin A / (1 + cos A) =  1/√5 (1 + 2/ √5)

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So the answer is:

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Multiplying this by  √5 - 2 / √5 - 2 we get:

(2(5 - 4) + √5 - 2) /  (5 -4)

=  2 + √5 - 2 / 1

= √5.

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