XYZ IS AN ISOSCELES TRIANGLE \XY/=\XZ/=6CM AND YXZ=100 CALCULATE \YZ/ CORRECT TO 2s.f
9.2
use the law of cosines
YZ2 = 62 + 62 - 2*6*6*cos100°
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To calculate the length of YZ in an isosceles triangle XYZ with given values, we can use the Law of Cosines. The formula for the Law of Cosines is:
c² = a² + b² - 2ab*cos(C)
Where:
- c is the length of the side opposite the angle we are interested in (YZ in this case).
- a and b are the lengths of the other two sides (XY and XZ in this case).
- C is the angle opposite the side we are interested in (angle YXZ in this case).
In this problem, we are given that XY = XZ = 6 cm, and YXZ = 100 degrees. We need to calculate YZ, which is the side opposite the angle YXZ. Let's substitute the values into the formula and solve for YZ:
YZ² = 6² + 6² - 2 * 6 * 6 * cos(100)
YZ² = 36 + 36 - 72 * cos(100)
YZ² = 72 - 72 * cos(100)
Now, let's calculate the value of cos(100) using the trigonometric function in a calculator:
cos(100) ≈ -0.17364817766693033 (rounded to 15 decimal places)
Substituting this value back into the equation:
YZ² = 72 - 72 * (-0.17364817766693033)
YZ² = 72 + 12.480982416016222
YZ² ≈ 84.48098241601622
Taking the square root of both sides to solve for YZ:
YZ ≈ √84.48098241601622
YZ ≈ 9.2 cm (rounded to 2 significant figures)
Therefore, the length of YZ in the isosceles triangle XYZ is approximately 9.2 cm when rounded to 2 significant figures.