The equation $\cos ^{-1}\left(\frac{3.4}{10}\right)=x$ can be used to determine the measure of angle BAC.

What is the degree measure of angle BAC? Round to the nearest whole degree.

Find the value of x in radians using the inverse cosine function: x = cos − 1 ( 10 3.4 ​ ) .
Convert x from radians to degrees by multiplying by π 180 ​ .
Calculate the degree measure: x ≈ 70.123 degrees.
Round the degree measure to the nearest whole degree: 7 0 ∘ ​ .

Explanation

Problem Analysis We are given the equation cos − 1 ( 10 3.4 ​ ) = x , which allows us to find the measure of angle BAC. Our goal is to find the degree measure of angle BAC, rounded to the nearest whole degree.

Find x in radians First, we need to find the value of x in radians by evaluating the inverse cosine function: x = cos − 1 ( 10 3.4 ​ ) .

Convert radians to degrees Next, we convert the value of x from radians to degrees. We know that 1 radian = π 180 ​ degrees . Therefore, we multiply x by π 180 ​ to convert it to degrees.

Calculate the degree measure Using a calculator, we find that cos − 1 ( 10 3.4 ​ ) ≈ 1.224 radians. Converting this to degrees, we have 1.224 × π 180 ​ ≈ 70.123 degrees.

Round to the nearest whole degree Finally, we round the degree measure to the nearest whole degree. Since 70.123 is closer to 70 than to 71 , we round down to 70 degrees.

Final Answer Therefore, the degree measure of angle BAC is approximately 7 0 ∘ .


Examples
Imagine you're building a ramp and need to determine the angle of elevation. If the ratio of the adjacent side to the hypotenuse is 3.4/10, you can use the inverse cosine function to find the angle in radians, then convert it to degrees for practical use in construction.

Answered by GinnyAnswer | 2025-07-08

The measure of angle BAC, calculated using cos − 1 ( 10 3.4 ​ ) , is approximately 66 degrees when rounded to the nearest whole degree.
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Answered by Anonymous | 2025-08-23