In a triangle the length of the side opposite the angle which measures 30 degree is 12 cm, what is the length of the side opposite to the angle which measures 60 degree?
A) 9 cm B) 12√3 cm C) (15√3)/2 cm D) (9√3)/2 cm
Answers
Answer:
In a triangle the length of the side opposite the angle which measures 45 degrees is 8cm. What is the length of the side opposite to the angle which measures 90 degrees?
Method 1:
It is an isosceles right triangle. So if the side opposite the 45 deg angle is 8 cm , the other side will also be 8 cm. So the side opposite the 90 deg, or hypotenuse is [8^2+8^2]^0.5 = (64+64)^0.5 = 128^0.5 = 11.3137085 cm.
Method 2:
By the sine formula we have the relation
a/sin A = b/sin B = c/sin c [Let <C = 90 deg]
8/sin 45 = 8/sin 45 = c/sin 90, or
c = 8*sin 90/sin 45 = 8*1/0.707106781 = 11.3137085 cm.
Method 3:
By the cosine formula we have the relation
c^2 = a^2 + b^2 + 2 ab cos C
c^2 = 8^2 + 8^2 + 2*8*8*cos 90 = 64 + 64 + 0 = 128, so
c = 128^0.5 = 11.3137085 cm.
Method 4:
Area of the triangle = (side^2)/2
Area of the isosceles right triangle = 8*8/2 = 32 sq cm.
The altitude on the hypotenuse will be = half the hypotenuse.
Area = c* altitude on c/2 = c*half the c/2
= c^2 /4 = 32, or
c^2 = 4*32 = 128, or hypotenuse (or c) = 128^0.5 = 11.3137085 cm.
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