Use the inverse trigonometric functions on a calculator to find the measure of angle A in degrees. Round the answer to the nearest whole number.
Understand the Problem
The question asks to find the measure of angle A in a right triangle, given the length of the opposite side (23 m) and the hypotenuse (33 m). We will solve for the angle using the inverse sine function (arcsin) to find the angle whose sine is equal to the ratio of the opposite side to the hypotenuse. The answer should be rounded to the nearest whole number.
Answer
$A \approx 44^{\circ}$
Answer for screen readers
$A \approx 44^{\circ}$
Steps to Solve
- Identify the trigonometric ratio
Since we are given the opposite side and the hypotenuse, we will use the sine function. $ \sin(A) = \frac{opposite}{hypotenuse} $
- Substitute the given values
Substitute the given values of the opposite side (23 m) and the hypotenuse (33 m) into the equation. $ \sin(A) = \frac{23}{33} $
- Find the inverse sine
To find the measure of angle A, we need to use the inverse sine function (arcsin). $A = \arcsin(\frac{23}{33})$
- Calculate the angle using a calculator
Using a calculator, compute the arcsin of $\frac{23}{33}$: $A \approx 44.10^{\circ}$
- Round to the nearest whole number
Round the answer to the nearest whole number. $A \approx 44^{\circ}$
$A \approx 44^{\circ}$
More Information
The inverse sine function is used to find the angle when you know the ratio of the opposite side to the hypotenuse in a right triangle.
Tips
A common mistake is using the wrong trigonometric function (cosine or tangent) or forgetting to use the inverse trigonometric function. Also, make sure your calculator is in degree mode. Another common mistake is not rounding to the nearest whole number as the question specifies.
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