The hypotenuse of a 45°-45°-90° triangle measures 10 sqrt 5 in. What is the length of one leg of the triangle?

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05-07-2017
Mathematics

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The hypotenuse of a 45°-45°-90° triangle measures 10 sqrt 5 in. What is the length of one leg of the triangle?

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bcalle bcalle · Answer 1 · 2017-07-05T04:35:10+02:00

There is one rule to remember for 45-45-90 right triangle: hyp = sqrt2 * leg
Given the hypotenuse, plug the value into the equation and solve.

10sqrt5 = sqrt2 * leg
Divide both sides by sqrt2

10sqrt5
----------- = leg
sqrt2

Multiply the numerator and denominator by sqrt2 to clear the radical..
(10sqrt5)(sqrt2) 10 sqrt10 5sqrt10 = leg
-------------------- = leg -------------- = leg
(sqrt2)(sqrt2) 2

samuelonum1 samuelonum1 · Answer 2 · 2022-04-20T12:27:23+02:00

Applying the SOH CAH TOA Method, the Length of the Opposite side was gotten as 15.81 inch

Mensuration of Triangle

Given Data

Lenght of hypotenuse = 10√5 inch

Since the triangle is a right Triangle, we can apply the SOH CAH TOA method to get the other sides of the triangle

Sin θ = Opp/Hyp

Sin 45° = Opp/10√5

Making the Opp Subject of formula we have

Opp = Sin 45° * 10√5

Opp = 0.7071 * 22.360

Opp = 15.81 Inch

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