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Alex787 [66]
3 years ago
12

LMN≅PQR What is the value of x in degrees?

Mathematics
2 answers:
astra-53 [7]3 years ago
5 0
180-39-55=86°
...........................
DENIUS [597]3 years ago
4 0

Since angle LMN = angle PQR, angle M = angle Q

Since angle Q = 55 degrees, Angle M also = 55 degrees

We know that the three angles of a trainangle should be equal to 180 degrees

So, L + M + N = 180

Angle L is the unkown x

x + 55 + 39 = 180

x +94 =180

x = 180-94

x = 86 degrees

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Forces of 9 lbs and 13 lbs act at a 38º angle to each other. Find the magnitude of the resultant force and the angle that the re
fiasKO [112]

Answer: R=20.84\ lb\quad 22.57^{\circ},15.43^{\circ}

Step-by-step explanation:

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Two forces of 9 and 13 lbs acts 38^{\circ} angle to each other

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\Rightarrow R=\sqrt{9^2+13^2+2(9)(13)\cos 38^{\circ}}\\\Rightarrow R=\sqrt{81+169+184.394}\\\Rightarrow R=\sqrt{434.394}\\\Rightarrow R=20.84\ lb

Resultant makes an angle of

\Rightarrow \alpha=\tan^{-1}\left( \dfrac{b\sin \theta}{a+b\cos \theta}\right)\\\\\text{Considering 9 lb force along the x-axis}\\\\\Rightarrow \alpha =\tan^{-1}\left( \dfrac{13\sin 38^{\circ}}{9+13\cos 38^{\circ}}\right)\\\\\Rightarrow \alpha =\tan^{-1}(\dfrac{8}{19.244})\\\\\Rightarrow \alpha=22.57^{\circ}

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