In triangle abc and a 60 angle b 90 c 30 an root 3 then find ac
Answers
Step-by-step explanation:
aswer is
54/-A+52 = 90 /2 = 23
answer is 23
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∆ABC is a right triangle with angle B = 90° and C = 60°. Obviously, A = 30°. It's sides can be calculated either by using ratios and proportions or by trigonometry.
Algebraically, by Ratios and Proportions:
(30°,60°,90°) is a special right angle. One set square in the geometry box is of such a shape. What's the speciality about?
The sides of this right triangle is in the ratio of 1:√3:2.
That's 1x:√3x:2x. If one side is known, other sides can be calculated.
BC : AB : AC = 1x : √3x : 2x = a : c : b
BC = x = a = 8 cm is the shortest leg by data.
Hypotenuse = AC = b = 2x = 16 cm
AB = c = √3x = 8√3 cm, the larger leg.
By Trigonometry: The sine rule is an equation relating the lengths of the sides of a triangle to the sines of its angles.
By Sine Rule,
a/sin A = b/sin B = c/sin C
8/sin 30° = b/sin 90° = c/sin 60°
8/(½) = b/1 = c/(√3/2)
16 cm = b = AC
c = 8√3 cm = AB