Question

Calculate the area triangle MNO.
The base is 20 and the two sides are 13, and 15.
A. 9.9 units
B. 6.6 units
C. 97.5 units
D. 19.9 units

Answer 1

You need the height to calc the angle so calculate z. You then use the standard formula for triangle area.

Answer 2

i dont have a Y nor an X in the picture it gives me @Mandre

Answer 3

You need the height to calculate the area. I'm half asleep lol.

Answer 4

y is the height.

Answer 5

@Mandre, I aint gonna lie but i am too. Im drinking a crap ton of coffee

Answer 6

y and x I added to calculate the area. You cannot calculate the area without calculating the height unless you're working with a right-angled triangle and this time we are not.

Answer 7

\[y ^{2}=13^{2}-x ^{2}\]
\[y ^{2}=15^{2}-(20-x) ^{2}\]
That's using pythagoras. Are you with me?

Answer 8

I think I am with you

Answer 9

now you can set the last 2 parts = to each other as both equal y^@.
\[13^{2}-x ^{2}=15^{2}-(20-x) ^{2}\]
You can calculate x from that right?

Answer 10

y^2 that is.

Answer 11

It seems a good 'guestimate' is already sufficient. If you look at the sides 13 and 15, you would expect the diagonal (hypothenusa) to be roughly SQRT(13^2+15^2) if the angle N is roughly 90 degrees. Simple calculation shows that if N = 90 deg, the diagonal is 19.8, which is very close to 20. Let's assume this angle is 90 degrees.

If N = 90 degrees, the total area is 0.5 * (13 * 15) = 97.5, so answer C is the only one even close to what you would expect, without too much algebra.