Question

given that triangle LMN has side lengths of 18.5 inches, 10 inches, and 15.5 inches, prove triangle LMN is a right triangle. explain

Answer 1

A Triangle is right angled with one angle 90⁰

Step-by-step explanation:

Given Δ LMN has side has side lengths of 18.5 inches, 10 inches, and 15.5 inches.prove triangle LMN is a right triangle

Given:

Δ LMN has side lengths of 18.5 inches, 10 inches, and 15.5 inches

∠M = 90⁰ , right angled at 90⁰

To prove:

Δ LMN is a right triangle

Proof:

In Δ LMN,

∠L+ ∠M + ∠N = 180⁰ angle sum property in a triangle

∠L+ ∠90⁰+ ∠N = 180⁰ Given ∠90⁰ = M

∠L + ∠N = 180⁰ - 90⁰ = 90⁰

LN² = LM² + MN² Pythagoras theorem

LN = √( LM² + MN²) = Hypotenuse LM ⊥ MN

Δ LMN is right triangle proved

Answer 2

Hypotenuse^2 = opposite^2 + adjacent^2

Step-by-step explanation:

The diagram of the triangle has been attached to the solution.

Side length of the triangle: 18.5, 15.5, 10

To prove a right angle triangle, we would apply Pythagoras theorem

Hypotenuse^2 = opposite^2 + adjacent^2

Hypothenus is the longest side of a right angle triangle

Opposite is the length facing the angle theta at the base. Also referred to as the perpendicular

Adjacent is the base

Hyp^2 = opp^2 +adj^2

Hyp^2 = 18.5inches , opp= 15.5inches, adj= 10 inches

Hyp^2 = 18.5^2 = 342.25

opp^2 +adj^2= 15.5^2 + 10^2

= 100+240.25 =340.25

342.25 is not equal to 340.25

Since Hyp^2 is not equal to (opp^2+adj^2), it is not a right-angled triangle.

Except there is an error with the figures in the question, the lengths given in the triangle would not give a right angle triangle.