Solve the problem...

Mathematics

1 answer:

Gre4nikov [31]3 years ago

5 0

Answer:

x = 59
y = 16.64
z = 19.42

Step-by-step explanation:

The sum of angles in a triangle is 180°, so angle x is the complement of the one marked 31°.

x = 90 -31

x = 59

The tangent relation tells you ...

tan(31°) = 10/y

y = 10/tan(31°) = 10/0.6009

y ≈ 16.64

The sine relation tells you ...

sin(31°) = 10/z

z = 10/sin(31°) = 10/0.5150

z ≈ 19.42

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The point-slope form:

$y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points $(-4,\ -1)$ and $\left(\dfrac{1}{2},\ 3\right)$ .

Substitute:

$m=\dfrac{3-(-1)}{\frac{1}{2}-(-4)}=\dfrac{4}{4\frac{1}{2}}=\dfrac{4}{\frac{9}{2}}=4\cdot\dfrac{2}{9}=\dfrac{8}{9}\\\\y-(-1)=\dfrac{8}{9}(x-(-4))\\\\y+1=\dfrac{8}{9}(x+4)$

The standard form: Ax + By = C

$y+1=\dfrac{8}{9}(x+4)\qquad\text{multiply both sides by 9}\\\\9y+9=8(x+4)\qquad\text{use distributive property}\\\\9y+9=8x+32\qquad\text{subtract 9 from both sides}\\\\9y=8x+23\qquad\text{subtract 8x from both sides}\\\\-8x+9y=23\qquad\text{change the signs}\\\\\boxed{8x-9y=23}$