Question

Given a right triangle with legs a, b and hypotenuse c, solve for b if a= 72 and c= 75

a 21

b 3

c 441

d 104

Answer 1

The answer is a. 21.

Explanation:

We solve this question by using Pythagoras theorem to relate the sides of a right angled triangle.

Here,

Hypotenuse of the given triangle(c)=75

Two sides of right angled triangle are:

a=72

b=?

Then,

for a given right angled triangle abc,

Using Pythagoras theorem,

`c=\sqrt{a^(2) +b^(2) }`

Squaring on both sides,

`c^(2) =a^(2)+b^(2)`

or,
`75^(2)=72^(2)+b^(2)`

or,
`b^(2)=75^(2)-72^(2)`

or,
`b^(2)=5625- 5184`

or,
`b^(2) =441`

∴
`b=21`

So, the value of b is obtained to 21 by the use of Pythagoras theorem.