Multiple Choice
If = in a right triangle, what is the value of rounded to two decimal places?
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2. Trigonometric Functions on Right Triangles
Trigonometric Functions on Right Triangles
Multiple Choice
In right triangle , the angle bisector of is . If , what is the measure of ?
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Verified step by step guidance1
Identify the given elements: triangle \( \triangle PQR \) is a right triangle, and \( Q E \) is the angle bisector of angle \( \angle PQR \). This means \( \angle PQR \) is split into two equal angles by the segment \( Q E \).
Since \( Q E \) bisects \( \angle PQR \), the two angles formed at \( Q \) are equal. Given that \( m\angle PQE = 20^\circ \), it follows that \( m\angle EQ R = 20^\circ \) as well.
Therefore, the entire angle \( \angle PQR \) is the sum of these two equal angles: \( m\angle PQR = m\angle PQE + m\angle EQR = 20^\circ + 20^\circ \).
Recall that \( \triangle PQR \) is a right triangle, so one of its angles is \( 90^\circ \). Since \( \angle PQR \) is the angle being bisected, it must be less than \( 90^\circ \).
Conclude that \( m\angle PQR = 40^\circ \) by adding the two equal parts, which matches the sum of the two \( 20^\circ \) angles formed by the bisector.
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