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Math  /  Geometry

QuestionAnswer Attempt 1 out of 2 Estimated length of WX‾=7.5 cm\overline{W X}=7.5 \mathrm{~cm} The actual length of WX‾=\overline{W X}= □\square cm (round to 3 decimal places)

Studdy Solution

STEP 1

1. The triangle is a right triangle with legs measuring 4 cm and 6.3 cm.
2. The hypotenuse WX‾ \overline{WX} is the side opposite the right angle.
3. We will use the Pythagorean Theorem to calculate the length of the hypotenuse.

STEP 2

1. Identify the known sides of the triangle.
2. Apply the Pythagorean Theorem to find the length of the hypotenuse.
3. Round the calculated length to three decimal places.

STEP 3

Identify the lengths of the two legs of the right triangle. The legs are given as 4 cm and 6.3 cm.

STEP 4

Apply the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse c c is equal to the sum of the squares of the other two sides a a and b b :
c2=a2+b2 c^2 = a^2 + b^2
Substitute the known values:
c2=(4)2+(6.3)2 c^2 = (4)^2 + (6.3)^2

STEP 5

Calculate the squares of the lengths of the legs:
c2=16+39.69 c^2 = 16 + 39.69

STEP 6

Add the results to find c2 c^2 :
c2=55.69 c^2 = 55.69

STEP 7

Take the square root of both sides to solve for c c :
c=55.69 c = \sqrt{55.69}

STEP 8

Calculate the square root to find the length of the hypotenuse:
c≈7.459 c \approx 7.459

STEP 9

Round the calculated length to three decimal places. Since the calculated value is already at three decimal places, no further rounding is necessary.
The actual length of WX‾ \overline{WX} is:
7.459 cm \boxed{7.459} \, \text{cm}

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