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Allisa [31]
3 years ago
6

Determine the measures of all unknown angles and side lengths of PQP.

Mathematics
1 answer:
nirvana33 [79]3 years ago
6 0

Answer:

m∠R = 50°

PR ≈ 5.74

PQ ≈ 8.53

Step-by-step explanation:

ig

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6. Two observers, 7220 feet apart, observe a balloonist flying overhead between them. Their measures of the
MaRussiya [10]

Answer:

The ballonist is at a height of 3579.91 ft above the ground at 3:30pm.

Step-by-step explanation:

Let's call:

h the height of the ballonist above the ground,

a the distance between the two observers,

a_1 the horizontal distance between the first observer and the ballonist

a_2 the horizontal distance between the second observer and the ballonist

\alpha _1 and \alpha _2 the angles of elevation meassured by each observer

S the area of the triangle formed with the observers and the ballonist

So, the area of a triangle is the length of its base times its height.

S=a*h (equation 1)

but we can divide the triangle in two right triangles using the height line. So the total area will be equal to the addition of each individual area.

S=S_1+S_2 (equation 2)

S_1=a_1*h

But we can write S_1 in terms of \alpha _1, like this:

\tan(\alpha _1)=\frac{h}{a_1} \\a_1=\frac{h}{\tan(\alpha _1)} \\S_1=\frac{h^{2} }{\tan(\alpha _1)}

And for S_2 will be the same:

S_2=\frac{h^{2} }{\tan(\alpha _2)}

Replacing in the equation 2:

S=\frac{h^{2} }{\tan(\alpha _1)}+\frac{h^{2} }{\tan(\alpha _2)}\\S=h^{2}*(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})

And replacing in the equation 1:

h^{2}*(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})=a*h\\h=\frac{a}{(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})}

So, we can replace all the known data in the last equation:

h=\frac{a}{(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})}\\h=\frac{7220 ft}{(\frac{1 }{\tan(35.6)}+\frac{1}{\tan(58.2)})}\\h=3579,91 ft

Then, the ballonist is at a height of 3579.91 ft above the ground at 3:30pm.

6 0
3 years ago
Round 418 to the nearest ten.
marissa [1.9K]

Answer:

The answer should be 420.

~

Step-by-step explanation:

7 0
2 years ago
Joe has 80 stamps. 1/4 of the stamps are state stamps. How many state stamps does he have
Hitman42 [59]

Answer:

80/4

Step-by-step explanation:

You do \frac{80}{1} =\frac{1}{4} which is 80/4

8 0
3 years ago
If x = 3 and y = -1, what is the value of xy ÷ -3?
Mariulka [41]

Answer: 1

Step-by-step explanation:

First multiply x and y which is 3 x -1 = -3

Then -3 ÷ -3 = 1

7 0
3 years ago
PLS HELP!!! 20 POINTS!!!!!
sweet [91]

Answer:

the answer is D

Step-by-step explanation:

the answer will be D

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