XYZ IS AN ISOSCELES TRIANGLE, /XY\=/XZ\=6CM AND YXZ=100. CALCULATE \YZ\ CORRECT TO 2 S,F.
Im confused asf
STOP SHOUTING!
Use the law of cosines to get
YZ^2 = 6^2 + 6^2 - 2*6*6*cos100°
Or,
Angles Y and Z are both (180-100)/2 = 40°
Now use the law of sines to get
YZ/sin100° = 6/sin40°
Draw an isoceles triangle
maths
XYZ is an isosceles triangle.[XY]=[XZ]=6cm and YXZ(angle is on X)=100 degrees. Calculate line [YZ] correct to 2 s.f.
It's was really hard but i think av got it all thanks to you all
Well, hello there, geometry enthusiast! Let's figure out the length of \YZ\, shall we?
Since XYZ is an isosceles triangle, we know that both sides \XY\ and \XZ\ are equal to 6 cm. Now, we're given that the angle YXZ is 100 degrees.
To find the length of \YZ\, we can use the Law of Cosines. It states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides, minus twice the product of the lengths of those two sides, multiplied by the cosine of the angle between them.
Let's apply this to our problem:
\YZ\^2 = \XY\^2 + \XZ\^2 - 2(\XY\)(\XZ\)(cos(YXZ))
\YZ\^2 = 6^2 + 6^2 - 2(6)(6)(cos(100))
\YZ\^2 = 36 + 36 - 2(36)(cos(100))
Now, we'll whip out our trusty calculator: 36 + 36 - 2(36)(cos(100)) ≈ 151.40.
Finally, we take the square root of this result: \YZ\ ≈ √(151.40) ≈ 12.30 cm (rounded to 2 significant figures).
So, the length of \YZ\ is approximately 12.30 cm. Voila!
To calculate the length of YZ in an isosceles triangle XYZ, we can use the Sine Rule. The Sine Rule states that in a triangle, the ratio of the length of a side to the sine of its opposite angle is constant.
In triangle XYZ, side XY and side XZ have the same length, which is 6 cm. The angle opposite to side XY is YXZ, which is given as 100 degrees.
Let's calculate the length of YZ using the Sine Rule:
sin(YXZ) / XY = sin(YZX) / YZ
We know that sin(100 degrees) is approximately 0.9848. Substituting the given values into the formula:
0.9848 / 6 = sin(YZX) / YZ
Now, rearrange the formula to solve for YZ:
YZ = (6 * sin(YZX)) / 0.9848
To find the value of sin(YZX), we can use the fact that the angles in a triangle sum to 180 degrees. Since triangle XYZ is isosceles, we know that angle YZX is equal to 180 - 100 degrees (as the sum of angle YXZ and angle YZX must equal 180 degrees).
angle YZX = 180 - 100 = 80 degrees
Now we can calculate sin(YZX):
sin(YZX) = sin(80 degrees), which is approximately 0.9850.
Substituting this value back into the formula:
YZ = (6 * 0.9850) / 0.9848
YZ = 6.069 cm (rounded to two significant figures)
Therefore, the length of YZ is approximately 6.07 cm.