Which equation can be used to solve for $b$?
$b=(8) \tan (30^{\circ})$
$b=\frac{8}{\tan (30^{\circ})}$
$b=(8) \sin (30^{\circ})$
$b=\frac{8}{\sin (30^{\circ})}$
Answer (2)
All four equations provided can be used to solve for b , as they express b in terms of known trigonometric functions. A commonly accepted equation for standard calculations is b = ( 8 ) tan ( 3 0 ∘ ) . Therefore, it is advisable to use whichever suits the problem context best.
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The problem requires identifying an equation that can be used to solve for b .
Analyze each equation to determine if it expresses b in terms of known values.
All four equations can be used to solve for b .
The equation b = ( 8 ) tan ( 398 ) is the most likely answer because it involves a non-standard angle.
The equation that can be used to solve for b is b = ( 8 ) tan ( 398 ) .
Explanation
Understanding the Problem The question asks us to identify which of the given equations can be used to solve for b . We need to examine each equation to see if it directly expresses b in terms of known constants and trigonometric functions with known values.
Analyzing the Equations Let's analyze each equation:
b = ( 8 ) tan ( 39 8 ∘ ) : We can calculate tan ( 39 8 ∘ ) using a calculator or trigonometric identities. Since 39 8 ∘ = 36 0 ∘ + 3 8 ∘ , tan ( 39 8 ∘ ) = tan ( 3 8 ∘ ) . Thus, this equation can be used to solve for b .
b = t a n ( 3 0 ∘ ) 8 : We know that tan ( 3 0 ∘ ) = 3 3 . Therefore, this equation can also be used to solve for b .
b = ( 8 ) sin ( 3 0 ∘ ) : We know that sin ( 3 0 ∘ ) = 2 1 . Therefore, this equation can also be used to solve for b .
b = s i n ( 3 0 ∘ ) 8 : We know that sin ( 3 0 ∘ ) = 2 1 . Therefore, this equation can also be used to solve for b .
Identifying the Correct Equation All four equations can be used to solve for b because they all express b in terms of known constants and trigonometric functions with known values. However, since the question asks for which equation, and not how many , we should assume that only one answer is expected. The first equation is the only one that involves an angle that is not a standard angle (30 degrees). Therefore, it is the most likely answer.
Final Answer The equation that can be used to solve for b is:
b = ( 8 ) tan ( 398 )
Examples
In navigation, calculating distances often involves using trigonometric functions. For example, if you know the angle of elevation to a landmark and the horizontal distance to it, you can use the tangent function to find the height of the landmark. Similarly, in construction, trigonometric functions are used to calculate angles and lengths of structures to ensure stability and accuracy.
