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.
A. $19^{\circ}$
B. $20^{\circ}$
C. $70^{\circ}$
D. $71^{\circ}$
Answer (1)
Find the value of x by evaluating the inverse cosine: x = cos − 1 ( 10 3.4 ) .
Calculate the value of x in degrees: x ≈ 70.1 2 ∘ .
Round the value of x to the nearest whole degree: x ≈ 7 0 ∘ .
The degree measure of angle BAC is: 7 0 ∘ .
Explanation
Analyze the problem We are given the equation cos − 1 ( 10 3.4 ) = x and asked to find the degree measure of angle BAC, which is represented by x . We need to calculate the value of x in degrees and round to the nearest whole degree.
Find the cosine To find the value of x , we need to evaluate the inverse cosine of 10 3.4 . That is, we need to find the angle x such that cos ( x ) = 10 3.4 = 0.34 .
Calculate the inverse cosine Using a calculator, we find that x = cos − 1 ( 0.34 ) ≈ 70.1 2 ∘ .
Round to the nearest degree Rounding to the nearest whole degree, we get x ≈ 7 0 ∘ .
State the final answer Therefore, the degree measure of angle BAC is approximately 7 0 ∘ .
Examples
Understanding angles and inverse trigonometric functions is crucial in many real-world applications. For example, in architecture, engineers use these concepts to calculate the angles needed for constructing roofs or designing structures that can withstand specific loads. Similarly, in navigation, pilots and sailors use angles and trigonometry to determine their position and direction. In computer graphics, angles are used to rotate and position objects in 3D space, creating realistic and immersive experiences.
