Question

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

Answer 1

Answer:

b = 9.1units

Step-by-step explanation:

Find the diagram attached

Using the similarity theorem of triangle

WX/XZ = WY/WX

Substitute;

b/a+5 = 6/b

b² = 6(a+5) ... 1

Also according to pythagoras theorem on triangle WYX;

b² = 6²+a²...2  

Equate 1 and 2

6(a+5) = 6²+a²

6a+30 = 36 + a²

a²-6a+36-30 = 0

a²-6a+6 = 0

a = 6±√36+4(6)/2

a = 6±√60/2

a = 6±7.745/2

a = 13.745/2

a = 6.8725

Recall that

b² = 6²+a²

b² = 36+6.8725²

b² = 83.2313

b = 9.12units

b = 9.1units