(50 points) What is the value of x in the triangle?
1 answer:
Answer:
x = 23.78 cm to the nearest hundredth
Step-by-step explanation:
In a right-angled triangle:
The opposite "O" is the opposite side to the angle
The adjacent side "A" is adjacent side to the angle
The hypotenuse "H" is the long side that joins the 2 legs
For this triangle, we have:
angle = 18°
adjacent (A) = x
hypotensue (H) = 25
So we can use the trig formula:
Therefore,
Multiply both sides by 25: 25 cos(18) = x
Therefore, x = 23.77841291...
So x = 23.78 cm to the nearest hundredth
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The angle is in the second quadrant.
Step-by-step explanation:
The cosecant of an angle is the same as the reciprocal of the sine of that angle. In other words, as long as ,
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Consider a unit circle centered at the origin. If the terminal side of angle intersects the unit circle at point
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For angle ,
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, meaning that the intersection is above the
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In other words, this intersection is above and to the left of the origin. That corresponds to second quadrant of the cartesian plane.