In a right triangle, if one of the acute angles measures , what is the measure of the other acute angle?
Table of contents
- 0. Review of College Algebra4h 43m
- 1. Measuring Angles40m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
2. Trigonometric Functions on Right Triangles
Trigonometric Functions on Right Triangles
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Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
Given two right triangles, triangle and triangle , with right angles at and respectively, which angle has a sine ratio equal to ?
A
Angle in triangle
B
Angle in triangle
C
Angle in triangle
D
Angle in triangle
Verified step by step guidance1
Recall that in a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Mathematically, for an angle \( \theta \), \( \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \).
Identify the right angles in the triangles: \( \angle Q \) in triangle \( PQR \) and \( \angle T \) in triangle \( STU \). Since these are right angles, the other two angles in each triangle are acute and their sine ratios can be expressed using the sides adjacent and opposite to them.
Look at the given sine ratio \( \frac{p}{q} \). This ratio corresponds to the length of the side opposite the angle over the hypotenuse in one of the triangles. To find which angle has this sine ratio, examine the sides labeled \( p \) and \( q \) in the triangles and determine which angle's opposite side is \( p \) and hypotenuse is \( q \).
For triangle \( PQR \), if side \( PQ = p \) and side \( PR = q \) (assuming \( PR \) is the hypotenuse), then \( \sin(\angle P) = \frac{\text{opposite side to } P}{\text{hypotenuse}} = \frac{p}{q} \). Similarly, check the other triangle \( STU \) for the same ratio.
Conclude which angle corresponds to the sine ratio \( \frac{p}{q} \) by matching the opposite and hypotenuse sides in the triangles. This will identify the correct angle among the options given.
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