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Chapter 5: Problem 64

Explain how to find one of the acute angles of a right triangle if two sides are known.

Short Answer

Expert verified
To find one of the acute angles in a right triangle when two sides are known, you'll first need to identify which sides have been given, and then choose the correct trigonometric function (sine, cosine, or tangent) that incorporates these two sides. Then, plug the values into the trigonometric function, and find the angle by taking the inverse of this function. The right trigonometric function choice and the use of calculator accurately can help find the acute angle.

Step by step solution

01

Identify the sides of the right triangle

First, identify which sides of the triangle are given. The hypotenuse is the longest side and is opposite the right angle. The other two sides can be considered as the adjacent side to the angle you're looking to find, and the side opposite to this angle.
02

Choose the trigonometric function

Next, choose the trigonometric function that includes both given sides. If you're given the hypotenuse and the opposite side, for example, you'd use the sine function. If you're given the hypotenuse and the adjacent side, use the cosine function. If you're given the adjacent and the opposite sides, you'd use the tangent function.
03

Use the trigonometric function to find the angle

Once you know which trigonometric function to use, set up the equation with the given information. Then, solve for the angle by taking the inverse of the trigonometric function you've used (e.g. arcsin, arccos, or arctan) on your calculator.

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Most popular questions from this chapter

Use a right triangle to write each expression as an algebraic expression. Assume that \(x\) is positive and that the given inverse trigonometric function is defined for the expression in \(x\). $$ \sec \left(\sin ^{-1} \frac{x}{\sqrt{x^{2}+4}}\right) $$

Use a graphing utility to graph two periods of the function. $$y=0.2 \sin \left(\frac{\pi}{10} x+\pi\right)$$

Use a right triangle to write each expression as an algebraic expression. Assume that \(x\) is positive and that the given inverse trigonometric function is defined for the expression in \(x\). $$ \cot \left(\sin ^{-1} \frac{\sqrt{x^{2}-9}}{x}\right) $$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Using radian measure, I can always find a positive angle less than \(2 \pi\) coterminal with a given angle by adding or subtracting \(2 \pi\)

Will help you prepare for the material covered in the next section. $$ \text { Simplify: } \frac{-\frac{3 \pi}{4}+\frac{\pi}{4}}{2} $$
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