An isosceles triangle has two sides of length 27.8cm. The Angle opposite the base is 64 degrees. Find The Base

Question

im trying to find the base.

Answer 1

Well, one way, you can draw a line from the 64 degree angle to the base - which will give you a right triangle with one angle at 90 degrees, one angle at 32 degrees, and a hypotenuse of 27.8 cm.

1/2 base = 27.8 x cos32 = 23.575737

base = 47.15 cm

Answer 2

Well, it's an isosceles triangle, so you know two angles are the same--one angle is known to be 64 degrees. So take 180 and subtract 64. You get 116, divide this by two (for the two angles). You get 64, 58 and 58. Then use the law of sines to solve this. Your base equals: [(sin 64)(27.8cm)]/(sin 58). Your answer is (rounded off) 29.46 cm.

Answer 3

An isosceles triangle has two sides of length 27.8cm. The Angle opposite the base is 64°.

So the two base angles are (180 - 64)°/2 ie 58°

By sine rule

27.8 / sin58° = base / sin64°

So base = 27.8 sin64° / sin58°

≈ 29.5 cm

Answer 4

The vertex attitude chop up the isoceles triangle into 60-30-ninety triangles. opposite of the 60 degree attitude is the backside it relatively is 9 for each triangle. with the help of the Pythagoreom Thm, the section opposite of the 30 degree attitude is x/2 and the section opposite of the 60 degree attitude is xsqrt(3)/2. x = 18/sqrt(3) so the altitude the only opposite of the 30 degree attitude is in basic terms (18/sqrt(3))(a million/2) = 9/sqrt(3)

Answer 5

Law of Cosines.
c² = a² + b² - 2*a*b*cos(Φ) sound 'bout right?
I get 29.46 cm.


Doug