Question

1. zaid wants to hang the pennant shown vertically between two windows that are 19 inches apart. will the pennant fit? explain. enter your answer.

Explanation:

Step1: Identify the triangle type

The pennant is a right - triangle with hypotenuse \( c = 41\) inches and an acute angle of \(30^{\circ}\). We want to find the length of the side opposite the \(30^{\circ}\) angle (let's call it \(a\)), because this side will represent the height of the pennant (the vertical dimension we care about for fitting between the windows). In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). For \(\theta = 30^{\circ}\), \(\sin(30^{\circ})=\frac{1}{2}\).

Step2: Calculate the height of the pennant

Using the sine formula \(\sin\theta=\frac{a}{c}\), where \(\theta = 30^{\circ}\), \(c = 41\) inches. So \(a=c\times\sin(30^{\circ})\). Substituting the values, we get \(a = 41\times\frac{1}{2}=20.5\) inches.

Step3: Compare with the window separation

The distance between the two windows is 19 inches. Since \(20.5>19\), the pennant will not fit.

Answer:

The pennant will not fit because the height of the pennant (the side opposite the \(30^{\circ}\) angle in the right - triangle) is \(20.5\) inches, which is greater than the 19 - inch separation between the two windows.