# Thread: Trigonometry Perpendicular line help!?

1. ## Trigonometry Perpendicular line help!?

8. In a triange ABC, AB = 4.8cm, BC = 3.8 cm and A ^B C =42 degrees

P is the foot of the perpendicular from A to BC.
i. Calculate the area of triangle ABC

ii. Deduce the length of AP.

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Okay, I don't understand what they mean by "P is the foot of the perpendicular from A to BC"

2. ## Re: Trigonometry Perpendicular line help!?

did you make a sketch ... ?

from vertex A to side BC , AP is the altitude from A to BC.

also ...

... and A ^B C =42 degrees
what angle is this?

3. ## Re: Trigonometry Perpendicular line help!?

Okay thanks.

soo I worked out the area to be 61.02 usuing 1/2*a*b*sin C

now for part II i'm not sure what to do.. I know the angle is 90. can u give me a hint or guide me a bit? :S

4. ## Re: Trigonometry Perpendicular line help!?

Your area is 10 times greater than it should be. To find the altitude, simply use:

$\sin(42^{\circ})=\frac{\bar{AP}}{\bar{AB}}$

5. ## Re: Trigonometry Perpendicular line help!?

But i don't know what AP is!

6. ## Re: Trigonometry Perpendicular line help!?

oKAY I used Area= 1/2*base*height

and then i rearranged theformula to get the height as 3.7

correct?

7. ## Re: Trigonometry Perpendicular line help!?

You have:

$A=\frac{1}{2}\bar{BC}\cdot\bar{AB}\sin(42^{\circ})$

and:

$A=\frac{1}{2}\bar{BC}\cdot\bar{AP}$

Hence:

$\bar{AP}=\bar{AB}\sin(42^{\circ})$ (which you would get from my previous post)

$\bar{AP}\approx3.2\text{ cm}$