3 years ago

Help with these questions!

Mathematics

1 answer:

LekaFEV [45]3 years ago

8 0

Step-by-step explanation:

An inscribed angle is half the arc angle.

m∠MNQ = 80°/2

m∠MNQ = 40°

The angle between two chords is the average of the arc angles.

m∠AMB = (80° + 85°) / 2

m∠AMB = 82.5°

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If a = 7 and b = 11, what is the measure of ∠B? (round to the nearest tenth of a degree) A) 32.5° B) 39.2° C) 50.5° D) 57.5°

Ilia_Sergeevich [38]

Answer:

D) 57.5°

Step-by-step explanation:

As the question is not complete. So, let's suppose it is a right angle triangle then, we can apply Pythagoras theorem to calculate the hypotenuse or the third side.

Pythagoras Theorem = $c^{2}$ = $a^{2} + b^{2}$

a = 7 and b = 11

$a^{2}$ = 49

$b^{2}$ = 121

Plugging in the values, we will get:

$c^{2}$ = 49 + 121

$c^{2}$ = 170

c = $\sqrt{170}$

To calculate the unknown angle B, we can use law of sine.

Law of sine = $\frac{a}{sinA}$ = $\frac{b}{sinB}$ = $\frac{c}{sinC}$

So,

$\frac{c}{sinC}$ = $\frac{b}{sinB}$

$\frac{\sqrt{170} }{sin90}$ = $\frac{11}{sinB}$

Sin90 = 1

sinB = $\frac{11}{\sqrt{170} }$

B = $sin^{-1}$ ( $\frac{11}{\sqrt{170} }$ )

B = 57.5°

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Minimum: 6

Maximum: 81

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