math quest

[xoangelxo]

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Draw a triangle and call it ABC (do not draw a right triangle though). If AB is 16 and AC is 10 and angle BAC is 30 degrees, what is the area of triangle ABC????? Thanks! This is number 35 in quant reasoning in topscore test 3..i dont get their explanation though.

 

[marscole]

i got 48 cm^2 or mm^2 or in^2 (not unit was given)

 

[shane.]

Alright, since there are no replies yet i'm going to take the plunge.

Note that this is all off what I remember from math in high school.

Try drawing this out as I explain it. At point B I drew a line down making two right triangles to a new point between A and C let's call D. To find the height of this line (height of the triangle I will later use in the area formula) I used sin 30 = x/16 (SOH - CAH - TOA will never leave my mind) to find that x = 8. Now let's find length AD, since this will be used as part of our base in the area formula. Time to employ good ol' Pythagorean, 16^2 = 8^2 + AD^2 yields AD = 13.865 but let's call it 14. Now to the second part of our base length DC. 10^2 = 8^2 + DC^2 gives DC = 6. Sum AD and DC to get AC = 20.

Area of a triangle = 1/2(base)(height)
= 1/2(20)(8)
= 80

Am I correct?

My explanation may seem lengthy but this problem actually took me around a minute, maybe less.

Like I said I just winged it, so i'm likely wrong. Hopefully someone will correct me if I am.

 

[xoangelxo]

the answer is suppose to be 40. Topscore's explanation is:

Let x=16 and y=10
A=(1/2)xysinJ
(1/2)(10)(16)(sin30degrees)
80sin30
80(1/2)=40

I dont get it!?!

 

[laundry]

Ok, it's 40.

So you have your triangle drawn. Extend an altitude at a right angle to AC. Now you have a right tringle with the hypotenuse of 16 and an angle of 30.

To find the altitude you need to remember that the sides of a 30-60-90 triangle are (root 3), 1, and 2. So, the length of the altitude is 1/2 of the AB = 8.
Taking AC as base, we get 1/2(8 x 10) = 40

If you're lost, wait a couple of hours, I'll get home and attach a picture explanation.

Cheers, 👍

 

[shane.]

My bad, I had misread the question and though it was BC = 10. Not AC = 10.

 

[xoangelxo]

got it! Thanks..that wasnt bad =)

 

[Dotoday]

Yes the answer is 40. it is easy, they just didn`t show you one step. remember the area of a triangle is 1/2base*height. So if you have a triangle and one angle is known which is 30, and the other two sides are 10 and 16. The way they are telling you to label it is that base is 10. So all you need is to draw a vertical line from the angle ABC(which is the vertex of a triangle) and that will be your heght. Now, you use the formula sin30 = opposite/ hypotenuse. Opposite is X- the line you just drew and the hypotenuse is 16. So, sin30= x/16 and that gives you x = 8. So the your heght (vertical line) is 8. Your base is 10. So you have Area of a tringle = 1/2(Base)*(height), or
1/28*(10)*(8) = 5*8 = 40.
I hope this helps,
Good luck.

 

[Danny289]

Draw a triangle and call it ABC (do not draw a right triangle though). If AB is 16 and AC is 10 and angle BAC is 30 degrees, what is the area of triangle ABC????? Thanks! This is number 35 in quant reasoning in topscore test 3..i dont get their explanation though.

answer is 40 and it is very easy, just follow m direction:
1- draw the triangle appricate to what you have.( AB> AC AB=16 , AC=10)

2- <A = 30

3- now from point C draw a line, prependicular to AB, this line will have a cross with AB in one point we call that point D < D= 90 .

Now we have a triangle ACD that < D = 90 and < A =30 ( sin 30 =1/2=0.5)

4- in triangle ACD I can calculate CD HOW?

5- in triangle ACD ========> Sin < A = CD/AC===> 0.5=CD/10 ==> CD= 5

6- in ABC triangle CD is hight and BC is base (because CD is perpendicular on AB).
7- you know the area of triangle now 1/2( base X hight) ==> 1/2(5 X 16) ==>
Area=40 !