Question

In ΔLMN, ∠N is a right angle, LM = 76 units, and MN = 40 units. What is the approximate measure of ∠M?

Answer 1

58.2°

Explanation:

First we find the measure of LN using the Pythagorean theorem.

LM is across from angle N, which makes it the hypotenuse. This means that MN is a leg. In the Pythagorean theorem, this gives us

a²+40²=76²

a²+1600 = 5776

Subtract 1600 from each side:

a²+1600-1600 = 5776-1600

a² = 4176

Take the square root of each side:

√(a²) = √(4176)

a = 64.622

We will now use the sine ratio to find the measure of angle M. Sine is the ratio of the side opposite an angle to the hypotenuse; the side opposite M, LN, is 64.622, and the hypotenuse is 76:

sin M = 64.622/76

Taking the inverse sine of each side,

sin⁻¹(sin M) = sin⁻¹(64.622/76)

M = 58.24 ≈ 58.2°

Answer 2

The measure of ∠M is 58.2°

Explanation:

Given ΔLMN, ∠N is a right angle, LM = 76 units, and MN = 40 units. we have to find the approximate measure of ∠M.

As,
`cos{\theta}=(Base)/(Hypotenuse)={B}{H}`

Here,
`cos∠M=(40)/(76)=(10)/(19)`

⇒
`\angle M=cos^(-1)(10)/(19)=58.2431361407\sim58.2^(\circ)`

Hence, the measure of ∠M is 58.2°