One of the legs of a right triangle measures 4 cm and its hypotenuse measures 16 cm . Find the
measure of the other leg. If necessary, round to the nearest tenth.

Question

One of the legs of a right triangle measures 4 cm and its hypotenuse measures 16 cm . Find the measure of the other leg. If necessary, round to the nearest tenth.

UpStudy AI · Accepted Answer

To find the measure of the other leg of the right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Given:
- One leg of the right triangle measures 4 cm.
- The hypotenuse measures 16 cm.

Let's denote the length of the other leg as $$ x $$ cm.

Using the Pythagorean theorem:
$$ 4^2 + x^2 = 16^2 $$

Solving for $$ x $$:
$$ 16 + x^2 = 256 $$
$$ x^2 = 256 - 16 $$
$$ x^2 = 240 $$
$$ x = \sqrt{240} $$

Now, we need to round the value of $$ x $$ to the nearest tenth.
Calculate the value by following steps:
- step0: Calculate:
  $$\sqrt{240}$$
- step1: Write as a product:
  $$\sqrt{16\times 15}$$
- step2: Write in exponential form:
  $$\sqrt{4^{2}\times 15}$$
- step3: Use the properties of radicals:
  $$\sqrt{4^{2}}\times \sqrt{15}$$
- step4: Simplify the root:
  $$4\sqrt{15}$$
The measure of the other leg of the right triangle is approximately 15.5 cm when rounded to the nearest tenth.
The other leg of the right triangle is approximately 15.5 cm.

One of the legs of a right triangle measures 4 cm and its hypotenuse measures 16 cm . Find the
measure of the other leg. If necessary, round to the nearest tenth.

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