In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 1.5 meters and c = 2.2 meters, what is b? If necessary, round to the nearest tenth. b = _____ meters

To find the length of leg ( b ) in a right triangle when you know the lengths of leg ( a ) and the hypotenuse ( c ), you can use the Pythagorean theorem, which states:

[

a^2 + b^2 = c^2

]

Given:

– ( a = 1.5 ) meters

– ( c = 2.2 ) meters

First, we need to calculate ( c^2 ) and ( a^2 ):

1. ( c^2 = (2.2)^2 = 4.84 )
2. ( a^2 = (1.5)^2 = 2.25 )

Now, plug these values into the Pythagorean theorem:

[
2.25 + b^2 = 4.84

]

Now, subtract ( 2.25 ) from both sides:

[

b^2 = 4.84 – 2.25 = 2.59

]

To find ( b ), take the square root of ( b^2 ):

[

b = sqrt{2.59} approx 1.61 text{ meters}

]

When rounded to the nearest tenth:

[

b approx 1.6 text{ meters}

]

So, the length of leg ( b ) is approximately 1.6 meters.