Question

Find the value of x.

Answer 1

The answer is 45

Explanation:

Method 1

75-48=27

hyp²=opp²+adj²

x²=36²+27²

x²=1296+729

x²=2025

take square root of both sides

x=45

Method 2

hyp²=opp²+adj²

hyp²=36²+48²

hyp²=1296+2304

hyp²=3600

take the square root of both sides

hyp=60

hyp=opp

hyp²=opp²+adj²

adj²=hyp²-opp²

x²=75²-60²

x²=5625-3600

x²=2025

take square root of both sides

x=45

Answer 2

x = 45

Explanation:

Pythagoras Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

`\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}`

We can use Pythagoras Theorem to find the hypotenuse of the right triangle with legs measuring 36 and 48 units.

`\begin{aligned}36^2+48^2&=c^2\\1296+2304&=c^2\\3600&=c^2\\√(3600)&=√(c^2)\\c&=60\end{aligned}`

Therefore, the hypotenuse of the left right triangle is 60 units.

The hypotenuse of the left right triangle is the longest leg of the other right triangle (with hypotenuse of 75 units and shortest leg of x units).

Therefore, we can use Pythagoras Theorem again to find the value of x:

`\begin{aligned}x^2+60^2&=75^2\\x^2+3600&=5625\\x^2&=2025\\√(x^2)&=√(2025)\\x&=45\end{aligned}`

Therefore, the value of x is 45.