sin theta = -9/41, where theta is in Q IV; find the angle theta:
Here the opp side is -9, the hyp. is 41. The adj side is found by applying the Pyth. Thm.:
(-9)^2 + x^2 = 41^2
81 + x^2 = 1681. Then x^2 = 1600, and the adj. side (x) is +40. We know it's +40 because theta is in Q IV.
The angle theta is arcsin (-9/41). Using a calculator,
arcsin (-9/41) = -0.22 radians (which is correct because theta is in Q IV, just as -0.22 rad is in Q IV. You could express theta as a positive angle by subtracting 0.22 rad from 2pi rad: 1.78 rad. You could, of course, change these angles in radians into angles in degrees.
Take the right angled triangle with sides 13, 12 and 5. sine theta will be 12/13
When sin theta < 0 and cos theta < 0 we are in the third quadrant so sin theta will be -12/13
tan theta = sin theta / cos theta = -5/13 / -12/13 = -5*13 / -12*13 = 5/12
Answer
148cm^2
Explanation
A cuboid has equal width and length as it’s base is a square. So w or l = root 30
Since the volume of a cuboid is
Length • width • height
And we know length and width when multiplied are 30
30 • height = 120
Therefore height = 4
Now for surface area it’s
2 • h • l + 2 • h • w + 2 • l • w
2 • 4 • root 30 + 2 • 4 • root30 + 2 • 30 = 60 + 16root30 = 148~cm^2
Answer:
The width is 75.
Step-by-step explanation:
Since we already know that perimeter = width + length, then all we needed to do was subtract the length (15) from the perimeter (90) to get the width (75)!
Hope this helped!
Using Pythagoras theorem, we know that 3² + 4² = 5², draw the 3-foot side and the 4-foot side with a right angle between them. The 5-foot side will fit to form a right triangle
<h3>How to use Pythagoras theorem to prove a right triangle?</h3>
The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
Therefore,
c²= a²+ b²
where
- c = hypotenuse side
- a and b are the other legs.
Therefore,
3² + 4² = 5²
Hence,
Knowing that 3² + 4² = 5², draw the 3-foot side and the 4-foot side with a right angle between them. The 5-foot side will fit to form a right triangle
learn more on Pythagoras's theorem here: brainly.com/question/20462170
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