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lozanna [386]
3 years ago
12

If MN=14, NO=11, and QR=27, find the length of PQ. Round your answer to the nearest tenth if necessary. Figures are not necessar

ily drawn to scale.

Mathematics
1 answer:
allsm [11]3 years ago
4 0

Answer:

PQ = 34.4

Step-by-step explanation:

First, we know that the angles in a triangle add up to 180 degrees. Therefore, angle M = 48 and angle R = 74

Next, because there is a corresponding angle in each triangle, they are similar. This means that the ratios between corresponding sides are the same. For example, the side opposite angle O (MN) over the side opposite angle R (PQ) is equal to the side opposite angle N (OM) over the side opposite angle Q (RP)

This can be written as MN/PQ = OM/RP. Note that both the numerators are on the same triangle, and MN and PQ correspond, as well as OM and RP.

We are given MN, NO, and QR. Because NO is opposite a 48 degree angle (angle M) as well as QR (angle P), we can say that NO/QR = another ratio of a pair of corresponding sides. Because we want to find PQ, and both PQ and MN are opposite 74 degree angles, we can say that

NO/QR = MN/PQ

Thus,

11/27 = 14/PQ

multiply both sides by PQ to remove a denominator

PQ * 11/27 = 14

multiply both sides by 27 to remove the other denominator

PQ * 11 = 14 * 27

divide both sides by 11 to isolate the PQ

PQ = 14 * 27 /11

PQ = 34.4

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5 0
1 year ago
2.) Find the measure of exterior angle X:
Oxana [17]
ANSWER:
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6 0
2 years ago
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One plane can travel 30 miles per hour faster than another. one of them goes 185 miles in the same time it takes the other to go
ycow [4]
Plane #1 speed:  x mph
Plane #2 speed:  (x+30) mph

time = time becomes

170 mi        185 mi
---------- = --------------
      x             x+30

Solving for x, the speed of the slower plane, we get

170x + 5100 = 185 x
                                           5100
Then 15x = 5100, and x = ---------- (mi/hr) = 340 mph
                                              15

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3 years ago
An airplane is flying at 180mph. A jet flying at 330 mph leaves 1 hour later traveling in the same direction. How long will it t
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To solve this problem, let us first assign some variables. Let us say that:

v1 = velocity of airplane = 180 mph

t1 = time travelled by airplane

v2 = velocity of jet = 330 mph

t2 = time travelled by jet

 

Since we know that distance is the product of velocity and time, and that the distance travelled by the two must be equal for the jet to catch up to the plane, hence:

v1 * t1 = v2 * t2

But we know that:

t1 = t2 + 1

Therefore:

180 (t2 + 1) = 330 t2

180 t2 + 180 = 330 t2

150 t2 = 180

t2 = 1.2 hours

 

<span>Therefore the jet can catch up to the plane after 1.2 hours it takes off.</span>

4 0
3 years ago
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