Calvin is using a 10 foot ladder to paint his house. If he leans the ladder against the house so that it makes a 71° angle with the ground, how far up the house does the
ladder reach? Round to two decimal places.

9.46 ft

Step-by-step explanation:

Law of sines

10/sin(90)=x/sin(71)

x=(sin(71)*10)/sin(90)

x=9.46

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°