Y = mx + b, where m = slope = rise/run and b, the y intercept value

m = 1/1 = 1, then y = x + b.
We notice that y intercept is = - 1
And the equation is:

y = x - 1

6 0

3 years ago

What is one possible solution for the triangle below?

elixir [45]

Answer:

segment YZ ≈ 19.4 in
angle X ≈ 85.3°
angle Z ≈ 26.7°

Explanation:

1) Given two side lenghts and one angle you can use sine law:

$\frac{sinA}{a} = \frac{sinB}{b} = \frac{sinC}{c}$

2) Using the sides with length 43 in and 40in, and the corresponding opposite angles, Z and 68°, that leads to:

$\frac{sinZ}{43} = \frac{sin68}{40}$

From which you can clear sinZ and get:

sinZ = 43 × sin(68) / 40 = 0.9967

⇒ Z = arcsine(0.9967) ≈ 85.36°

3) The third angle can be determined using 85.36° + 68° + X = 180°

⇒ X = 180° - 85.36° - 68° = 26.64°.

4) Finally, you can apply the law of sine to obtain the last missing length:

$\frac{x}{sin(26.64)} = \frac{40}{sin(68)}$

From which: x = 40 × sin(26.64°) / sin(68°) = 19.34 in

The answer, then is:
segment YZ ≈ 19.4 in
angle X ≈ 85.3°
angle Z ≈ 26.7°

5 0

3 years ago

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