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Triangle Z W X is shown. Angle Z W X is a right angle. An altitude is drawn from point W to point Y on side Z X to form a right angle. The length of W X is b, the length of X Y is a, the length of Y Z is 5, and the length of W Y is 6.

What is the approximate value of b, rounded to the nearest tenth?

7.2 units
7.8 units
8.6 units
9.4 units

Triangle Z W X is shown. Angle Z W X is a right angle. An altitude is drawn from point-example-1
User Pkqk
by
8.7k points

2 Answers

3 votes

Answer:

b ≈ 9.4 units

Explanation:

User Jeffff
by
8.6k points
4 votes

Answer:

b ≈ 9.4 units

Explanation:

Δ WZY and Δ XWY are similar triangles, thus the ratios of corresponding sides are equal, that is


(XW)/(WZ) =
(XY)/(WY) =
(WY)/(ZY)

Calculate WZ using Pythagoras identity in right triangle WZY

WZ² = 5² + 6² = 25 + 36 = 61 ( take the square root of both sides )

WZ =
√(61) ≈ 7.81

Substituting value into the ratio


(XW)/(WZ) =
(WY)/(ZY)


(b)/(7.81) =
(6)/(5) ( cross- multiply )

5b = 46.86 ( divide both sides by 5 )

b ≈ 9.4 ( to the nearest tenth )

User Colin Steel
by
8.5k points

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