Find the Hypotenuse of a Right Triangle with One Angle Measuring 45° and Opposite Side Measuring 5 cm.

Answer – The length of the hypotenuse of the given right triangle is 7.071 cm.

Explanation:

The hypotenuse is the longest side of a right-angled triangle. It occurs opposite the right angle and can be found using a suitable trigonometric ratio when given one side and an angle.

The given right angled-triangle can be drawn as shown here:

A right triangle with one angle measuring 45 degrees and its opposite side measuring 5 cm

Since the measure of an angle is given with its opposite side, the sine ratio can be used to find the hypotenuse.

$\sin θ = \frac{O p p o s i t e s i d e}{H y p o t e n u s e}$

$\Rightarrow \sin 45 ° = \frac{A B}{A C}$

$\Rightarrow 0.7071 = \frac{5}{A C}$

$\Rightarrow A C = \frac{5}{0.7071}$

$\Rightarrow A C = 7.071 c m ≃ 7 c m$

Thus, the length of the hypotenuse of the given right triangle is $≃ 7 c m$ .

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Answer – The length of the hypotenuse of the given right triangle is 7.071 cm.

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