Find the values of x and y that make these triangles congruent by the HL theorem

A. x = 3, y = 2

Step-by-step explanation:

The hypotenuse and the length of one leg of one right triangle must be equal to the hypotenuse and corresponding length of the one leg of the other ∆ for both triangles to be equal by the HL Congruence Theorem.

Thus, let's find x and y by setting the corresponding lengths of the two right ∆s equal to each other.

Therefore:

x = y + 1 › eqn. 1

2x + 3 = 3y + 3 › eqn. 2

Substitute x = (y + 1) into eqn. 2, and solve for y.

2x + 3 = 3y + 3 › eqn. 2

2(y + 1) + 3 = 3y + 3

2y + 2 + 3 = 3y + 3

2y + 5 = 3y + 3

Collect like terms

2y - 3y = -5 + 3

-y = -2

Divide both sides by -1

y = 2

Substitute y = 2 into eqn. 1.

x = y + 1 › eqn. 1

x = 2 + 1

x = 3

for the free

< < < emily> > >

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west