Question

What is the length of NO in triangle AMNO, where the measure of angle A is 20°, the measure of angle N is 39°, and MN is 3 feet?

A) 2.5 feet
B) 3.8 feet
C) 4.2 feet
D) 5.7 feet

Answer 1

To find the length of side NO in triangle AMNO, with given angles and one side, apply the Law of Sines. Calculate the measure of the third angle and set up a ratio to find the length of side NO.

Step-by-step explanation:

The question seeks to determine the length of side NO in triangle AMNO, given the measures of two angles and one side. To solve this, we can use the Law of Sines, which states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides and angles in a triangle.

First, we must find the third angle's measure in triangle AMNO. Since the sum of the angles in any triangle is 180 degrees, angle O = 180 - 20 - 39 = 121 degrees. Using the Law of Sines:

1. sin(A)/a = sin(N)/n = sin(O)/o
2. sin(20°)/MN = sin(121°)/NO
3. sin(20°)/3 = sin(121°)/NO
4. NO = 3 * sin(121°)/sin(20°)

Calculating the ratio yields NO's length.