XYZ is an isosceles triangle.[XY]=[XZ]=6cm and YXZ(angle is on X)=100 degrees. Calculate line [YZ] correct to 2 s.f.
YZ = 2(6 sin50°)
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XYZ is an isosceles triangle.[XY]=[XZ]=6cm and YXZ(angle is on X)=100 degrees. Calculate line [YZ] correct to 2 s.f.
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To calculate the length of line [YZ] in the isosceles triangle XYZ, we can use the Law of Cosines.
The Law of Cosines states that for any triangle with sides a, b, and c, and angle C across from side c, the following equation holds:
c^2 = a^2 + b^2 - 2ab * cos(C)
In our case, we know that [XY] = [XZ] = 6 cm, and the angle YXZ = 100 degrees. We want to find the length of [YZ].
Substituting the values into the Law of Cosines equation, we get:
[YZ]^2 = 6^2 + 6^2 - 2 * 6 * 6 * cos(100)
Simplifying further:
[YZ]^2 = 36 + 36 - 72 * cos(100)
Now we can calculate the value using a scientific calculator or online tool.
[YZ]^2 ≈ 36 + 36 - 72 * (-0.17364817766693033)
[YZ]^2 ≈ 72 + 12.51828927801082
[YZ]^2 ≈ 84.51828927801082
To find the length of [YZ], we take the square root of both sides:
[YZ] ≈ √(84.51828927801082)
[YZ] ≈ 9.19 cm (rounded to 2 significant figures)
Therefore, the length of line [YZ] is approximately 9.19 cm.