Question

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 coming

Answer 1

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


`\sin(30) = (ab)/(96) \\ ab = 96 \sin(30) \\ ab = 48`

Answer 2

`AB=48\text{ cm}`

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.

`\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}`

`\text{sin}(30^(\circ))=(AB)/(96)`

`\text{sin}(30^(\circ))* 96=(AB)/(96)* 96`

`0.5* 96=AB`

`48=AB`

Therefore, AB is 48 cm.