Area of triangle and sector?

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Answer 1 · 2018-05-15T21:11:39

#1910# (3 s.f)

Area of a circle(sector) is #\frac{\theta * \pi*r^{2}}{360}#

where r is the radius, and #\theta# is the angle of the sector.

Firstly, we need to work out the radius of the sector, which we can use Pythagoras theorem, from the triangle we've been given.

Let that be #r#

Therefore #r = \sqrt{30^{2}+40^{2}}#

This gives us 50.

Therefore the area of the sector becomes:

#A_sec = \frac{60 * \pi * 50^{2}}{360}#

This simpliflies to #A_sec = \frac{1250*\pi}{3}#

Then the area of the triangle (half * base divided by 2) becomes 600.

And since the question is applied in real life, give it to 3 s.f, which goes to #A = 1910 #