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Consider right triangle △GHI below.
Which expressions represent the length of side HI?

Consider Right Triangle GHI Below Which Expressions Represent The Length Of Side HI class=

Sagot :

reinhard10158

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))

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