Studdy AI Logo
Math

QuestionFind the length of one leg of a 45∘−45∘−90∘45^{\circ}-45^{\circ}-90^{\circ} triangle with hypotenuse 22222 \sqrt{2} units.

Studdy Solution

STEP 1

Assumptions1. The triangle is a 45∘−45∘−90∘45^{\circ}-45^{\circ}-90^{\circ} triangle, also known as an isosceles right triangle. . The hypotenuse of the triangle measures 2222 \sqrt{} units.
3. In a 45∘−45∘−90∘45^{\circ}-45^{\circ}-90^{\circ} triangle, the length of the hypotenuse is \sqrt{} times the length of each leg (since the legs are of equal length).

STEP 2

We can express the length of the hypotenuse in terms of the length of one leg (let's call it aa) using the property of a 45∘−45∘−90∘45^{\circ}-45^{\circ}-90^{\circ} triangle.
Hypotenuse=a2Hypotenuse = a \sqrt{2}

STEP 3

Now, we can plug in the given value for the hypotenuse to solve for aa.
222=a222 \sqrt{2} = a \sqrt{2}

STEP 4

To solve for aa, we can divide both sides of the equation by 2\sqrt{2}.
a=2222a = \frac{22 \sqrt{2}}{\sqrt{2}}

STEP 5

implify the equation to find the length of one leg of the triangle.
a=2222=22a = \frac{22 \sqrt{2}}{\sqrt{2}} =22So, the length of one leg of the triangle is22 units.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord