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.
Answer (1)
Calculate the inverse cosine: x = cos − 1 ( 10 3.4 ) .
Find the value in degrees: x ≈ 70.12 6 ∘ .
Round the result to the nearest whole degree: x ≈ 7 0 ∘ .
The measure of angle BAC is: 7 0 ∘ .
Explanation
Analyze the problem We are given the equation cos − 1 ( 10 3.4 ) = x , which we need to solve for x to find the measure of angle BAC in degrees. The problem asks us to round the answer to the nearest whole degree.
Calculate the inverse cosine To find the value of x , we need to calculate the inverse cosine of 10 3.4 .
x = cos − 1 ( 10 3.4 ) x = cos − 1 ( 0.34 ) Using a calculator, we find the value of x in degrees: x ≈ 70.12 6 ∘
Round to the nearest degree Now, we round the value of x to the nearest whole degree: x ≈ 7 0 ∘ Therefore, the degree measure of angle BAC is approximately 7 0 ∘ .
State the final answer The degree measure of angle BAC, rounded to the nearest whole degree, is 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 0.34, you can use the inverse cosine function to find the angle. In this case, the angle would be approximately 70 degrees, allowing you to build the ramp at the correct angle.
