Question

Let FGHB a right triangle with right angle G and an altitude as shown find XYZ

Answer 1

Part 1)
`z=4√(2)\ units`

Part 2)
`x=18\ units`

Part 3)
`y=12√(2)\ units`

Explanation:

step 1

Find the value of z

In the smaller right triangle IFG of the figure

Applying the Pythagoras Theorem

`6^(2)=2^(2)+z^(2)`

`z^(2)=6^(2)-2^(2)`

`z^(2)=32`

`z=4√(2)\ units`

step 2

In the right triangle HFG

Applying the Pythagoras Theorem

`x^(2)=y^(2)+6^(2)`

`y^(2)=x^(2)-36` -----> equation A

step 3

In the right triangle HIG

Applying the Pythagoras Theorem

`y^(2)=z^(2)+(x-2)^(2)`

`y^(2)=32+(x-2)^(2)` -----> equation B

step 4

equate equation A and equation B

`x^(2)-36=32+(x-2)^(2)\\x^(2)-36=32+x^(2)-4x+4\\4x=36+36\\4x=72\\x=18\ units`

step 5

Find the value of y

Substitute the value of x in the equation B

we have

`x=18\ units`

`y^(2)=32+(18-2)^(2)`

`y^(2)=32+(16)^(2)`

`y^(2)=288`

`y=12√(2)\ units`