Textbook Question
Solve each right triangle. In Exercise 46, give angles to the nearest minute. In Exercises 47 and 48, label the triangle ABC as in Exercises 45 and 46.
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2. Trigonometric Functions on Right Triangles
Solving Right Triangles
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Given the right triangle below, calculate all missing angles in degrees (round your answer to 3 decimal places.
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Verified step by step guidance1
Identify the given right triangle with sides labeled as 3 and 6, and the right angle at the bottom left corner.
Recall that in a right triangle, the sum of the angles is always 180 degrees. Since one angle is 90 degrees, the sum of the other two angles must be 90 degrees.
Use the tangent function to find angle y. The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. Here, tan(y) = opposite/adjacent = 3/6 = 0.5.
Calculate angle y using the inverse tangent function: y = tan^(-1)(0.5). This will give you the measure of angle y in degrees.
Once you have angle y, calculate angle x by subtracting angle y from 90 degrees, since x + y = 90 degrees in a right triangle.
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