Question 192725: One angle of an isosceles triangle has measure 150*. If the area of the triangle is 9 cm ^2, what is the perimeter to three significant digits?
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! the isosceles triangle with one angle of 150 deg, tells us that the vertex angle is 150, side angles are each 15 deg , for a total of 180 deg (150+15+15)
If side angle was 150, 2*150=300, oversize for triangle (180 deg)
If we sketch this triangle, and include an altitude h, base =(2b), and sides =a
we can figure Area =9(given) = (1/2) base * height
9=(1/2) (2b) (h)
but height is related to base thru 150 deg angle, or 15 deg angle.
from sketch ( just make a rough sketch, obtuse isosceles triangle) h/b = tan 15
or h=(tan15)(b)=.268(b), substituting into Area eqn
9=(1/2) (2b) (.268b)=.268 *b^2
dividing both sides by .268
9/.268 =b^2
33.582=b^2
taking sq rt
5.795 =b
but h=.268b=.268*5.795=1.5529
last side a can be found from, h/a = sin 15, or a=h/sin15 =1.5529/.2588=6
sides of triangle are a, a, and 2b, or 6,6,11.590
per = sum of sides = 23.590 ANSWER
checking area , a=(1/2) (11.590) (1.5529) =9 ok
to check sides, pythagorous can be used, 6^2=1.5529^2 + 5.795^2=6^2 ok
|
|
|
