Pls answer fully with explanation

Question

a shed is 8ft wide. One raft er makes an angle of 30 degrees with horizontal on one side of the roof.A raft er on the other side makes an angle of 70 degrees with the horizontal. Calculate the length of the shorter rafter to the nearest foot.

Answer 1

the width of the shed is one side of a triangle and the rafters are the other two sides of the triangle

draw the triangle and label as follows:

 

triangle ABC, top angle A, right side angle B, and left side angle C

bottom side a (8 feet), right side (rafter) c, left side (rafter) b

the law of sines is: a/sinA=b/sinB=c/sinC

8/sin80º=c/sin30º (or you could have used b/sin70º)

find sin 80º

sin 80º=0.9848

find sin 30º

sin 30º=0.5

substitute into the equation

8/(0.9848)=c/(0.5)

8.12347=c/0.5

c=8.12347*0.5

c=4.0617 feet (answer)

find the other rafter length...

b/sin70º=8/0.9848

b/0.93969=8/0.9848

b/0.93969=8.12347

b=8.12347*0.93969

b=7.6335 feet