Multiple Choice
Given a right triangle with angle and the side opposite to has length , the side adjacent to has length , and the hypotenuse has length , which equation can be used to find the measure of angle ?
2. Trigonometric Functions on Right Triangles
Trigonometric Functions on Right Triangles
Multiple Choice
In right triangle , angle measures . What is the measure of angle in degrees?
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Verified step by step guidance1
Identify the triangle involved and the angles given. We have a right triangle \( \triangle PSQ \) and an angle \( \angle PSR \) measuring \( 99^\circ \).
Recall that the sum of angles around a point is \( 360^\circ \). Since \( \angle PSR \) and \( \angle PSQ \) share vertex \( S \), consider how these angles relate to each other and the right angle in \( \triangle PSQ \).
Note that \( \triangle PSQ \) is a right triangle, so one of its angles is \( 90^\circ \). The sum of the other two angles in the triangle must be \( 90^\circ \) because the total sum of angles in any triangle is \( 180^\circ \).
Use the fact that \( \angle PSR \) and \( \angle PSQ \) are supplementary or complementary based on their geometric arrangement. Set up an equation relating \( \angle PSQ \) to \( \angle PSR \) and the right angle.
Solve the equation for \( \angle PSQ \) by subtracting the known angles from \( 180^\circ \) or \( 90^\circ \), depending on the relationship established, to find the measure of \( \angle PSQ \).
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