Question

Solve for the values of x and y

Answer 1

SOLVING LEFT-SIDED RIGHT TRIANGLE

Answer:

The value of the missing length of the side x=26 units

Explanation:

The Pythagorean theorem states

`\:a^2\:+\:b^2\:=\:x^2`

We will use the Pythagorean Theorem to solve for the missing side length.

`24^2\:+\:10^2\:=\:x^2`

switch both sides

`x^2=24^2+10^2`

`x^2=576+100`

`\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=√(f\left(a\right)),\:\:-√(f\left(a\right))`

`x=√(676),\:x=-√(676)`

`x=26,\:x=-26`

As x can not be negative.

Therefore, the value of the missing length of the side x=26 units

SOLVING LEFT-SIDED RIGHT TRIANGLE

Answer:

The value of the missing length of the side y=15 units

Explanation:

Considering the right-sided right triangle

The Pythagorean theorem states

`a^2\:+\:b^2\:=\:c2`

We will use the Pythagorean Theorem to solve for the missing side length.

`15^2\:+\:y^2\:=\:\left(15√(2)\right)^2`

`225+y^2=450` ∵
`\left(15√(2)\right)^2=450`

`y^2=225`

`y=√(225),\:y=-√(225)`

`y=15,\:y=-15`

As y can not be negative.

Therefore, the value of the missing length of the side y=15 units