Question

In ARST, S = 58 inches, ZR = 115º, and ZS = 19°. Find the length of r, to the nearest 10th of an inch.

a) 38.4 inches
b) 40.2 inches
c) 35.6 inches
d) 45.8 inches

Answer 1

The length of r, to the nearest tenth of an inch, is 38.4 inches. Option A is answer.

Step-by-step explanation:

In triangle RST, we have the following information:

S = 58 inches

ZR = 115 degrees

ZS = 19 degrees

We need to find the length of r, to the nearest 10th of an inch.

First, we can find the remaining angle, RS, using the fact that the angles in a triangle add up to 180 degrees:

RS = 180 degrees - ZR - ZS

RS = 180 degrees - 115 degrees - 19 degrees

RS = 46 degrees

Next, we can use the law of sines to find the length of r:

r/s = sin(RS)/sin(ZS)

r = s * sin(RS)/sin(ZS)

r = 58 inches * sin(46 degrees)/sin(19 degrees)

r = 38.4 inches (rounded to the nearest tenth of an inch)

Therefore, the length of r is 38.4 inches. Option A is answer.