Hello,(adsbygoogle = window.adsbygoogle || []).push({});

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

**Physics Forums | Science Articles, Homework Help, Discussion**