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30 POINTS NEED URGENT HELP

Use your trigonometry knowledge to answer the following question.

ABC is a right angled triangle. if B = 90°, AC = 96 cm, C = 30°.

AB =
cm
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30 POINTS NEED URGENT HELP Use your trigonometry knowledge to answer the following question ABC is a right angled triangle if B 90 AC 96 cm C 30 AB cm Image com class=

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aosera
Use SOH CAH TOA [pick one]


Since AC is hypotenuse [the length opposite of the right angle]
C is 30°.

We're finding AB.
So, we use SOH

[tex] \sin(30) = \frac{ab}{96} \\ ab = 96 \sin(30) \\ ab = 48[/tex]

Answer:

[tex]AB=48\text{ cm}[/tex]

Step-by-step explanation:

We have been given an image of a right triangle. We are asked to find the value of AB.

We can see that from our given diagram that angle C is opposite angle of side AB and side AC is hypotenuse of our given triangle.

We know that sine relates opposite side of a right triangle with its hypotenuse.

[tex]\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]

[tex]\text{sin}(30^{\circ})=\frac{AB}{96}[/tex]

[tex]\text{sin}(30^{\circ})\times 96=\frac{AB}{96}\times 96[/tex]

[tex]0.5\times 96=AB[/tex]

[tex]48=AB[/tex]

Therefore, AB is 48 cm.

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