A ladder 35 foot long is leaning against an embankment, inclined 62.5 degrees to the horizontal. if the bottom of the ladder is 10.2 feet from the embankment, what is the distance from the top of the ladder down to the embankment to the ground?

2 answers

Draw a diagram. If we label the triangle ABC, with sides a,b,c then the law of sines tells us

sinC/10.2 = sin117.5°/35
Now you have angles B and C, so you know A=180-(B+C)

a/sinA = sin117.5°/35
or
a^2 = 35^2+10.2^2 - 2*35*10.2 cosA
A 38 ft long ladder is leaning against an embankment inclined at 60 deg. to the horizontal. If the bottom of the ladder is 15 ft from the embankment, what is the distance from the top of the ladder down to the embankment to the ground?