Assume that Angle A is an acute angle and [tex]\tan A = 1.230[/tex]. What is the measure of Angle A?
Answer (3)
To find the measure of angle A when given that the tangent (tan) of angle A is 1.230, one must use the inverse tangent function, often denoted as tan-1 or arctan. This function allows you to calculate an angle when you know the tangent of that angle. In a scientific calculator, you input the tangent value to get the angle in degrees. If angle A is acute, and TAN A = 1.230, then the measure of angle A is given by:
Angle A = tan-1(1.230)
By performing this calculation, you would find the measure of angle A in degrees. Since the problem specifies that angle A is acute, we know that its measure should be between 0 and 90 degrees.
The measure of angle A is approximately 50.0 1 ∘ ,[/tex]calculated by finding the inverse tangent of 1.230.
the process step by step:
Step 1:
Recall the definition of the tangent function in a right triangle.
In a right triangle, the tangent of an acute angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
Step 2:
Substitute the given value of \tan(A) \
We are given that \tan(A) = 1.230 \
Step 3:
Inverse tangent to find the angle.
To find the measure of angle A \ we need to take the inverse tangent (or arctan) of 1.230, denoted as \tan^{-1}(1.230) \
Step 4:
Use a calculator to find the inverse tangent.
Calculating [tex] tan − 1 ( 1.230 ) gives us the measure of angle A in degrees.
Step 5:
Interpret the result.
The calculated value represents the measure of angle A ,[/tex] which is approximately 50.01^\circ \
Therefore, the measure of angle A \) is approximately [tex]\( 50.01^\circ \ obtained by finding the inverse tangent of 1.230.
The measure of angle A, given tan A = 1.230 , is approximately 50.0 1 ∘ , calculated using the inverse tangent function. This process involves applying the definition of the tangent function and using a scientific calculator. Thus, angle A is found by taking tan − 1 ( 1.230 ) .
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