Begin solving the triangle by using the Law of Sines to determine the angle B. sin A sin B a b sin 70° sin B 7 sin B = 5 5 sin 70° 7 5 sin 70° 7 There are two angles B, 0°
Begin solving the triangle by using the Law of Sines to determine the angle B. sin A sin B a b sin 70° sin B 7 sin B = 5 5 sin 70° 7 5 sin 70° 7 There are two angles B, 0°
Begin solving the triangle by using the Law of Sines to determine the angle B. sin A sin B a b sin 70° sin B 7 sin B = 5 5 sin 70° 7 5 sin 70° 7 There are two angles B, 0°
How do you get the smaller angle and bigger angle of B?
Transcribed Image Text:To solve the triangle using the Law of Sines, we need to determine angle \( B \).
Start by applying the Law of Sines:
\[
\frac{\sin A}{a} = \frac{\sin B}{b}
\]
Substitute the given values:
\[
\frac{\sin 70^\circ}{7} = \frac{\sin B}{5}
\]
Solve for \(\sin B\):
\[
\sin B = \frac{5 \sin 70^\circ}{7}
\]
This equation shows that there are two possible angles \( B \) where \( 0^\circ < B < 180^\circ \). Let \( B_1 \) be the smaller angle and \( B_2 \) the larger angle:
\[
B_1 \approx 42.16^\circ \quad \text{and} \quad B_2 \approx 137.84^\circ
\]
Explanation:
The text describes how to use trigonometry, specifically the Law of Sines, to find the angles in a triangle given one angle and two sides. The two possible solutions for angle \( B \) result from the sine function's property that \(\sin \theta = \sin (180^\circ - \theta)\).
Figure in plane geometry formed by two rays or lines that share a common endpoint, called the vertex. The angle is measured in degrees using a protractor. The different types of angles are acute, obtuse, right, straight, and reflex.
![To solve the triangle using the Law of Sines, we need to determine angle \( B \).
Start by applying the Law of Sines:
\[
\frac{\sin A}{a} = \frac{\sin B}{b}
\]
Substitute the given values:
\[
\frac{\sin 70^\circ}{7} = \frac{\sin B}{5}
\]
Solve for \(\sin B\):
\[
\sin B = \frac{5 \sin 70^\circ}{7}
\]
This equation shows that there are two possible angles \( B \) where \( 0^\circ < B < 180^\circ \). Let \( B_1 \) be the smaller angle and \( B_2 \) the larger angle:
\[
B_1 \approx 42.16^\circ \quad \text{and} \quad B_2 \approx 137.84^\circ
\]
Explanation:
The text describes how to use trigonometry, specifically the Law of Sines, to find the angles in a triangle given one angle and two sides. The two possible solutions for angle \( B \) result from the sine function's property that \(\sin \theta = \sin (180^\circ - \theta)\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff462e736-7a38-4abe-8728-e08b1ac68dd9%2F52729b50-3255-4afd-856c-eba663f520d1%2Fe5ewavs_processed.jpeg&w=3840&q=75)
