7 x [(26 - 5) - (5 + 6)]
1 answer:
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Answer:
<em>The helicopter is 27.38 m far off the ground</em>
Step-by-step explanation:
The drawing shown in the image below has all the measures and variables needed to solve the problem.
We need to find R, the height of the helicopter. We'll use the law of sines to find the length of side a.
The angle X is the measure needed to complete 180°:
X = 180° - 54° - 62° = 64°
Solving for a:
Calculating:
a = 31.11 m
Now using the sine ratio in the right triangle to the left side:
Solving for R:
R=31.11*0.88
R = 27.38 m
The helicopter is 27.38 m far off the ground
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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