Question

A=63°

C = 7.75 inch
B = 47°
Oblique Triangle
13. Refer to the oblique triangle shown. What's the length of side a? Round to the nearest hundredth of an inch.
O A. 7.75 inches
O B. 7.35 inches
O C.4.72 inches
O D. 6.03 inches

Answer 1

B. 7.35 inches

Explanation:

In the triangle:

• A=63°
• c = 7.75 inch
• B = 47°

Now we know that:

`\angle A+\angle B+\angle C=180^\circ$ (Sum of angles in a \triangle)\\63^\circ+47^\circ+\angle C=180^\circ\\\angle C=180^\circ-(63^\circ+47^\circ)\\\angle C=70^\circ`

Using the Law of Sines

`(a)/(\sin A) =(c)/(\sin C)\\\\(a)/(\sin 63^\circ) =(7.75)/(\sin 70^\circ) \\\\a=(7.75)/(\sin 70^\circ) * \sin 63^\circ\\\\a=7.35$ inches (to the nearest hundredth of an inch)`