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2 years ago

PLEASE HELP!!!!!!!!! Make sure you show all your work for full points. What is o?

Mathematics

2 answers:

Pie2 years ago

6 0

Answer:

o = 54

Step-by-step explanation:

The angle sum theorem tells you the sum of angles in a triangle is 180°. The definition of a linear pair tells you the two angles of a linear pair total 180°. Together, these relations tell you that an exterior angle of a triangle is equal to the sum of the remote interior angles.

In this geometry, the angle marked 78° is exterior to the left-side triangle. That means ...

78° = o° +24°

o° = 78° -24° = 54°

The value of 'o' is 54.

Additional comment

n° is the supplement of 78°, so is 102°.

m° is the difference between 102° and 22°, so is 80°.

Wittaler [7]2 years ago

4 0

Answer:

Step-by-step explanation:

M = 180 - (78 + 22)

M= 80

n = 180 - 78

N= 102

o = 180- (24 + 102)

O = 54

Hope this helped.

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3 years ago

A 51-foot wire running from the top of a tent pole to the ground makes an angle of 58° with the ground. If the length of the ten

AfilCa [17]

Answer:

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Step-by-step explanation:

This given situation can be thought of as triangle $\triangle PQR$ where PQ is the length of pole.

PR is the length of rope.

and QR is the distance of bottom of pole to the point of fastening of rope to the ground.

And $\angle Q \neq 90^\circ$

Given that:

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To find:

Side QR = ?

Solution:

We can apply Sine Rule here to find the unknown side.

Sine Rule:

$\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}$

Where

a is the side opposite to $\angle A$

b is the side opposite to $\angle B$

c is the side opposite to $\angle C$

$\dfrac{PR}{sinQ}=\dfrac{PQ}{sinR}\\\Rightarrow sin Q =\dfrac{PR}{PQ}\times sinR\\\Rightarrow sin Q =\dfrac{51}{44}\times sin58^\circ\\\Rightarrow \angle Q =79.41^\circ$

Now,

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Let us use the Sine rule again:

$\dfrac{QR}{sinP}=\dfrac{PQ}{sinR}\\\Rightarrow QR =\dfrac{sinP}{sinR}\times PQ\\\Rightarrow QR =\dfrac{sin42.59}{sin58}\times 44\\\Rightarrow QR = 35.11\ ft$

So, the answer is 35.11 ft.

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