triangle abc is right angled at C. if a=18 and ∠A=65. find b, c and ∠B
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triangle abc is right angled at C. if a=18 and ∠A=65. find b, c and ∠B
triangle abc is right angled at C. if a=18 and ∠A=65. find b, c and ∠B
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Step-by-step explanation:
Since triangle ABC is right angled at C, we can use trigonometric ratios to find the lengths of sides b and c.
First, we can use the sine ratio:
sin(A) = opposite/hypotenuse
sin(65°) = b/c
We can rearrange this to get:
b = c*sin(65°)
Next, we can use the Pythagorean theorem:
a^2 + b^2 = c^2
We can substitute the expression for b that we just found:
18^2 + (c*sin(65°))^2 = c^2
We can simplify this equation to get:
c^2 - (c*sin(65°))^2 = 18^2
c^2*(1 - sin^2(65°)) = 18^2
c^2*cos^2(65°) = 18^2
c = 18/cos(65°)
c ≈ 46.4
Now we can use the sine ratio again to find the length of side b:
b = c*sin(65°)
b ≈ 41.7
Finally, we can use the fact that the sum of the angles in a triangle is 180° to find the measure of angle B:
∠B = 90° - ∠A
∠B = 90° - 65°
∠B = 25°
Therefore, the lengths of sides b and c are approximately 41.7 and 46.4, respectively, and the measure of angle B is approximately 25°.