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))
