solve for x, y, z. right triangles.

Question

right triangles;  1) base=45, altitude=28, x degrees opposite 90 degrees.  2) 2nd triangle:  base= blank, hypotenuse=85, altitude=77.  z degrees opposite 90 degrees. y degrees is top of triangle

Answer 1

Usually when we talk about an angle being across from something in a triangle, it's across from a side, not another angle. So, it's not quite clear what angles x, y, and z represent, but I'll make my best guess. I'm assuming:

 

x is across from the 28-unit side in Triangle 1

y is across from the blank side in Triangle 2

z is across from the 77-unit side in Triangle 2

 

We'll use the Trigonometric functions to solve for x, y, and z.

 

 

 

x:

 

x is across from 28 and adjacent to 45. So, use tangent:

 

tan(x) = opposite/adjacent

tan(x) = 28/45

x = tan^-1(28/45)

x = 31.89°

 

 

 

y:

 

y is adjacent to 77 and the triangle's hypotenuse is 85. So, use cosine:

 

cos(y) = adjacent/hypotenuse

cos(y) = 77/85

y = cos^-1(77/85)

y = 25.06°

 

 

 

z:

 

z is opposite 77 and the triangle's hypotenuse is 85. So, we could use sine, or we could remember that a triangle's angles add up to be 180°. So:

 

90° + y + z = 180°

90° + 25.06° + z = 180°

115.06° + z = 180°

z = 64.94°