Step-by-step explanation:
since it is right-angled, first of all Pythagoras :
c² = a² + b²
c being the Hypotenuse (the side opposite of the 90 degree angle).
so,
8.3² = 8² + HI²
HI² = 8.3² - 8²
HI = sqrt(8.3² - 8²) = sqrt(68.89 - 64) = sqrt(4.89)
alternative : the law of sine
a/sin(A) = b/sin(B) = c/sin(C)
with the sides are always opposite of the associated angles.
angle G = 180 - 90 - 75 = 15° (as the sum of all angles in a triangle is always 180°).
so,
8.3/sin(90) = 8.3/1 = HI/sin(15)
HI = 8.3 × sin(15)
another alternative would be the extended Pythagoras for non-right-angled situations. like making HI the baseline, although the opposing angles G is not 90°.
c² = a² + b² - 2ab×cos(C)
C being the angle opposite of c.
HI² = 8.3² + 8² - 2×8.3×8×cos(15) = 132.89 - 132.8×cos(15)
HI = sqrt(132.89 - 132.8×cos(15))
For the scale factor, use the dimensions from similar sides:
Using 18 from the original image you would use 6 from the scaled image.
18 /6 = 3
This means the scaled image is 3 times smaller than the original. Because the scaled image is smaller divide 1 by the scale factor to get 1/3.
Q2:
The scale factor is 1 inch = 12 miles.
Multiply the total inches by 12:
6.5 x 12 = 78 miles.
Answer:
685,000
Step-by-step explanation:
The equations of the asymptotes of the given hyperbola are; y = ±(40/9)x
<h3>How to Interpret the equation of a hyperbola?</h3>
We are given;
Vertex at (0,−40)
Focus at (0, 41).
Thus, the equation of the asymptote of the given hyperbola is;
y = ±(40/(√41 - (-40))
y = ±(40/(√81)
y = ±40/9
Read more about Hyperbola Equation at; brainly.com/question/13003184
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Good luck on your assignment and enjoy your day!
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