Question

question 10 (multiple choice worth 1 point) louise is trying to find a rectangular canvas for his art project. its diagonal must measure 23.3 inches and form a 31° angle with the bottom of the canvas. what is the height of the canvas? round your answer to the nearest inch.

Explanation:

Step1: Use sine - function in right - triangle

In a right - triangle formed by the height $h$, the base, and the diagonal of the rectangular canvas, $\sin\theta=\frac{h}{d}$, where $\theta$ is the angle between the diagonal and the base, $h$ is the height of the canvas, and $d$ is the length of the diagonal.
We know that $\theta = 31^{\circ}$ and $d = 23.3$ inches.

Step2: Solve for the height

$h=d\times\sin\theta$.
Substitute $\theta = 31^{\circ}$ and $d = 23.3$ into the formula: $h = 23.3\times\sin(31^{\circ})$.
Since $\sin(31^{\circ})\approx0.515$, then $h=23.3\times0.515 = 12.0095\approx12$ inches.

Answer:

12 inches