Is 0.709 better than 0.81 or is it twisted around?
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Using 3 different methods, we can find that YZ = 25m
The complete image of a triangle is attached with the answer below.
<h3>What is trigonometry?</h3>The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
For a given triangle rectangle with a known angle θ and a hypotenuse H, we can write the trigonometric relations
sin(θ) = (opposite cathetus)/H
cos(θ) =(adjacent cathetus)/H
tan(θ) =(opposite cathetus)/(adjacent cathetus)
Now, in the given image we can see that:
θ = 30°
H = 50m
XY = adjacent cathetus
YZ = opposite cathetus.
We want to find YZ, so with the known things, we can use the first relation:
Sin 30 = YZ / 50
YZ = 50 x Sin30 = 25 meters
Now let's try another way.
We know that the sum of the internal angles of a triangle is always equal to 180°
In a triangle rectangle, we always have an angle equal to 90°.
Then the missing angle for our triangle can be computed from:
Z + 90° + 30° = 180°
Z = 180° - 90° - 30° = 60°
From this angle, the side YZ is the adjacent cathetus, then we can use the second trigonometric relation:
Cos 60 = YZ / 50
YZ = 50 x Cos 60 = 25 meters
Third way.
Whit the same angle we could find the side XY, the opposite cathetus, with:
Sin 60 = XY / 50
XY = 50Sin 60 = 43.3 meters
Now that we know one of the catheti, we can use the last trigonometric relation
tan 60 = XZ / YZ = 43.3 / YZ
YZ = 43.3 / tan 60 = 25 meters
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Answer:
x -5y = -20
Step-by-step explanation:
One way to write the equation for a line through two points is to use the slope formula. The slope is the same everywhere on a line, so the slope between the given points is the same as the slope between one of them and the general (x, y) point.
m = (y2 -y1)/(x2 -x1)
m = (5 -3)/(5 -(-5)) = (y -3)/(x -(-5))
2/10 = (y -3)/(x +5)
x +5 = 5(y -3) . . . . . . . multiply by 5(x+5)
x -5y = -20 . . . . . . rearranged to standard form
