Acute angle and triangle trigonometry

Question

1) Solve for the unknown side length.

x. =    10.0

___     ____

sin 30  Sin 80

 

 

2) In triangle UVW, angle U=50 degrees, v=19.4cm, V=45 degrees. Determine the length of side u .

 

3) In triangle XYZ, x=18cm, y =14cm, and z=17cm. Determine the measure of angle Y

Answer 1

1.  You have set up the problem using the law of sines, so just solve for x:

 

x = sin(30°) * 10 / sin(80°) = 5.08

 

 

2.  From the law of sines, u / sin(50) = 19.4 / sin(45)

 

 

u = 19.4 x sin(50°) / sin(45°) = 21.0 cm

 

 

 

3.  Use the law of cosines, y² = x² + z² - 2xz cos(Y)

 

 

cos(Y) = (x² + z² - y²) / (2xz) = (18² + 17² - 14²) / (2*18*17)

 

 

Y = cos^-1(417/612) = 47.0°