The measure of angle BAC can be calculated using the equation $\sin ^{-1}\left(\frac{3.1}{4.5}\right)=x$.
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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)
The measure of angle BAC is approximately 44 degrees, calculated using the inverse sine of the ratio 4.5 3.1 . After finding the result and rounding it to the nearest whole degree, we arrive at the final answer. The correct choice is 4 4 ∘ .
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Calculate the inverse sine of the ratio 4.5 3.1 .
Convert the result from radians to degrees.
Round the result to the nearest whole degree.
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 objective is to find the value of x in degrees, rounded to the nearest whole degree.
Calculating the angle To find the value of x , we need to calculate the inverse sine of 4.5 3.1 and then convert the result from radians to degrees.
The result of the calculation is approximately 43.54221902815587 degrees.
Rounding to the nearest degree Now, we round the calculated value to the nearest whole degree: 43.54221902815587 ≈ 44
Therefore, the measure of angle BAC is approximately 4 4 ∘ .
Final Answer The measure of angle BAC, rounded to the nearest whole degree, is 4 4 ∘ .
Examples
Imagine you are building a ramp and need to determine the angle of elevation. If the height of the ramp is 3.1 meters and the length of the ramp is 4.5 meters, you can use the inverse sine function to find the angle. This ensures the ramp is safe and functional for its intended use.
