Question

Match each missing side length and angle with the correct value.

Answer 1

Given:

• YM = 15

,

• YN = 8

,

• LN = 10

Let's solve for the missing side lengths and angles.

We have the following:

• Measure of angle NLY:

Since traingle NLY is a right traingle, to find the measure of angle NLY, apply trigonometric ratio.

Here, let's apply the trigonometric ratio formula for sine:

`sim\theta=(opposite)/(hypotenuse)`

Where:

θ is the angle

opposite side is the side opposite the angle = YN = 8

Hypotneuse = LN = 10

Thus, we have:

`\begin{gathered} sin(\angle NLY)=(8)/(10) \\ \\ sin(\angle NLY)=(4)/(5) \\ \\ \text{ Take the sine inverse of both sides:} \\ \angle NLY=sin^(-1)((4)/(5))=53.13^o \end{gathered}`

Therefore, m∠NLY = 53.13°.

• Measure of angle NMY:

Apply the trigonometric ratio formula for tangent:

`tan\theta=\frac{opposite}{\text{ adjacent}}`

Where:

θ is the angle

The opposite side is the side opposite the angle = YN = 8

Adjacent side is the side adjacent the angle = YM = 15.

Thus, we have:

`\begin{gathered} tan(\angle NMY)=(8)/(15) \\ \\ \text{ Take the tan inverse of both sides:} \\ \angle NMY=tan^(-1)((8)/(15)) \\ \\ \angle NMY=28.07^o \end{gathered}`

Therefore, m∠NMY = 28.07°.

• Length of NM:

To find the length of NM, apply Pythagorean Theorem:

`\begin{gathered} NM=√(8^2+15^2) \\ \\ NM=√(64+225) \\ \\ NM=√(289) \\ \\ NM=17 \end{gathered}`

The length of NM is 17.

• Length of LY:

To find the length of LY, also apply Pythagorean theorem:

`\begin{gathered} LY=√(10^2-8^2) \\ \\ LY=√(100-64) \\ \\ LY=√(36) \\ \\ LY=6 \end{gathered}`

ANSWER:

• m∠NLY ==> 53.13°

,

• m∠NMY ==> 28.07°

,

• NM ==> 17

,

• LY ==> 6