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Below are two questions i am unsure of. :uhh: Can someone please verify my answers and tell me if i am doing something wrong. :yuck: thank-you for your help.

1. A rigid beam 30 m long is leaning against a vertical wall. If the bottom of the beam is pulled horizontally away from the wall at 3 m/s, how fast is the angle between the beam and the ground changing when the bottom of the beam is 18 m from the wall?

sinθ = y/30

cosθ = 18/30

θ= 53.13

A= bh/2

A= [(x)(30sinθ)] / 2

A'= [(30sinθ) (dx/dt) + (x)(30cosθ) (dθ/dt)] / 2

0= [30sin(53.13) (3) + (18)(30cos53.13) (dθ/dt)] / 2

dθ/dt= -6.67 m/s

2.Triangle ABC is inscribed in a semicircle with diameter BC=12 cm. Find the value of angle B that produces the triangle of maximum area.

Hint: An angle inscribed in a semi-circle is a right triangle.

A=bh/2

A=(12cosB)(12sinB)

=72(2cosBsinB)

=72(sin2B)

A'=72(cos2B)

0=72cos2B

cos2B=0

2B=90°

B=45°

i got sin2B using the trig double angle forumla sin2x=2sinxcosx

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# Sliding ladder leaning against wall, and a triangle of maximum area

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