Question

Find each of the following angles for the given ratio. (0.25 points each) Angle Measure Trig Function sin X = 0.7547 sin A = 0.4540 cos Y = 0.5736 cos B = 0.5000 tan B = 0.6249 tan C = 0.1405

Answer 1

To find the angles corresponding to the given trigonometric ratios, we can use the inverse trigonometric functions. Here are the values calculated for each case:

1. For \( \sin X = 0.7547 \):
\[
X = \arcsin(0.7547) \approx 49.48^\circ
\]

2. For \( \sin A = 0.4540 \):
\[
A = \arcsin(0.4540) \approx 27.07^\circ
\]

3. For \( \cos Y = 0.5736 \):
\[
Y = \arccos(0.5736) \approx 54.75^\circ
\]

4. For \( \cos B = 0.5000 \):
\[
B = \arccos(0.5000) \approx 60.00^\circ
\]

5. For \( \tan B = 0.6249 \):
\[
B = \arctan(0.6249) \approx 32.49^\circ
\]
(Note: The previously calculated \( B \) from \( \cos B = 0.5000 \) is consistent with \( B \approx 60^\circ \), so ensure to clarify the context of \( B \) used.)

6. For \( \tan C = 0.1405 \):
\[
C = \arctan(0.1405) \approx 8.06^\circ
\]

In summary:

- \( X \approx 49.48^\circ \)
- \( A \approx 27.07^\circ \)
- \( Y \approx 54.75^\circ \)
- \( B \approx 60.00^\circ \)
- \( B \approx 32.49^\circ \) (if considering tan)
- \( C \approx 8.06^\circ \)