The measure of angle BAC can be calculated using the equation $\sin ^{-1}\left(\frac{3.1}{4.5}\right)=x$. What is the measure of angle BAC? Round to the nearest whole degree.
A. $0^{\circ}$
B. $1^{\circ}$
C. $44^{\circ}$
D. $48^{\circ}$
Answer (2)
Calculate the arcsin of the given ratio: sin − 1 ( 4.5 3.1 ) ≈ 0.7599 radians.
Convert the angle from radians to degrees: 0.7599 × π 180 ≈ 43.5 4 ∘ .
Round the result to the nearest whole degree: 43.5 4 ∘ ≈ 4 4 ∘ .
The measure of angle BAC is 4 4 ∘ .
Explanation
Problem Analysis We are given that the measure of angle BAC, denoted as x , can be calculated using the equation sin − 1 ( 4.5 3.1 ) = x . Our goal is to find the value of x in degrees, rounded to the nearest whole degree.
Calculate the arcsin value in radians First, we need to calculate the value of x using the inverse sine function (also known as arcsin) with the given ratio 4.5 3.1 . The result of sin − 1 ( 4.5 3.1 ) is approximately 0.7599 radians.
Convert radians to degrees Next, we convert the angle from radians to degrees. To do this, we multiply the radian value by π 180 . So, x ≈ 0.7599 × π 180 ≈ 43.54 degrees.
Round to the nearest whole degree Finally, we round the value of x to the nearest whole degree. Since 43.54 is closer to 44 than to 43 , we round up to 44 degrees. Therefore, the measure of angle BAC is approximately 4 4 ∘ .
Examples
Imagine you're building a ramp and need to determine the angle of elevation. If the rise of the ramp is 3.1 meters and the length of the ramp is 4.5 meters, you can use the arcsin function to find the angle. This ensures the ramp is safe and meets the required specifications.
The measure of angle BAC, calculated using sin − 1 ( 4.5 3.1 ) , is approximately 4 4 ∘ after converting it from radians to degrees and rounding. Therefore, the correct answer is C .4 4 ∘ .
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