Question

Find the value of each variable for the right triangles. Make sure all answers are in reduced radical form. Show your work.

Answer 1

By the Pythagorean theorem:

#1

`t= √(13^2-12^2)= √(169-144)= √(25)=5`

#2

`a= √(12^2-9^2)= √(144-81)= √(63)= √(9*7)=3 √(7)`

#3

`x= √(6^2+9^2)= √(36+81)= √(117)= √(9*13)=3 √(13)`

Answer 2

i) t = 5

ii) a = 3√7

iii) x =3√13

Explanation:

We have right triangles.

Know the two sides of the triangle and need to find the third missing side.

In order to find the third side of the right triangle, we use pythagoras theorem.

It is,

(Hypotenuse)² = (base)² + (height)²

i)

13² = 12² + t²

169 = 144 + t²

t² = 25

t = 5.

ii)

12² = 9² + a²

144 = 81 + a²

144 - 81 = a²

a² = 63

a = √63

iii)

x² = 9² + 6²

x² = 81 + 36

x² = 117

x = √117

x = 3√13