Right Angle
Right Angle
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How do you find the missing angle of a right Triangle using trigonometry?
it has one right angle, the opposite side is 34, and the hypotenuse is 55. I need to know HOW to do it, not just the answer. I know it's something with a inverse sin or something, i have a scientific calculator, and i'm in grade ten.
the formula for the angle of a right triangle is
sin x = height / hypotenuse
cos x = base / hypoteuse
now assume ABC is a triangle and A, B, and C are the angle and AB, AC, BC are the sides
now if you consider AC as hypotenuse and B as the right angle then
either, BC = heigh and AB = base [ the angle you will get is A related to AC and AB]
or, BC = base and AB = height [the angle you will get is C related to AC and BC]
that means using above formula you will get the angle of a right triangle related to hypotenuse and it's base, so it gives you opposite angle of the height
now the rest of the thins is depend upon which angle you want to measure, because there are two angle accept the right angle that are unknown
that means if you consider 34 as base you will get one angle and if you consider 34 as height you will get another angle
x = arcsin ( 34/55) [34 = height] [which is an opposite angle height]
x = arccos (34/55) [34 = base] if you do this the you need to subtract the value from 180 to get opposite angle as the angle you will get is related to base and hypotenuse
opp angle = 180 - arccos(34/55)