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.
Answer (2)
The measure of angle BAC is approximately 43 degrees, calculated by taking the inverse sine of 4.5 3.1 , converting it from radians to degrees, and rounding to the nearest whole number.
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Calculate the arcsin of the ratio: arcsin ( 4.5 3.1 ) .
Convert the result from radians to degrees by multiplying by π 180 .
Round the degree value to the nearest whole number.
The measure of angle BAC is approximately: 4 4 ∘ .
Explanation
Problem Analysis We are given the equation sin − 1 ( 4.5 3.1 ) = x , where x represents the measure of angle BAC in radians. Our goal is to find the measure of angle BAC in degrees, rounded to the nearest whole degree.
Calculate x in radians First, we need to calculate the value of x in radians. The result of the inverse sine function, sin − 1 ( 4.5 3.1 ) , gives us the angle in radians whose sine is 4.5 3.1 .
Convert radians to degrees Next, we convert the angle from radians to degrees. To do this, we use the conversion factor π 18 0 ∘ . So, we multiply the radian value by this factor to get the angle in degrees.
Calculate and round to nearest degree After performing the calculation, we find that the angle in degrees is approximately 43.67 degrees. Rounding this to the nearest whole degree, we get 44 degrees.
Final Answer Therefore, the measure of angle BAC, rounded to the nearest whole degree, is 44 degrees.
Examples
Imagine you're building a ramp for skateboarding. You know the height you want to reach (3.1 meters) and the length of the ramp's surface (4.5 meters). Using the arcsin function, you can calculate the angle of the ramp relative to the ground. This helps ensure the ramp is neither too steep nor too shallow for a safe and enjoyable ride.
