Question

The doorway in Julie's house is 80 inches tall, and the angle that the diagonal makes with the side of the doorway is 35° as shown in the diagram. Julie has a table top that is 8 feet long. She wants to know if she can move it through the door by leaning it to fit through the door diagonally. What is the length of the diagonal of Julie's doorway to the nearest tenth of an inch?

Answer 1

Explanation:

Use cos(adjacent/Hypotenuse) convert 80 inches by dividing by 12 feet. You get 6.6667 then ➗by cos 35 answer 8.13 rounded

Answer 2

The length of the diagonal will be given by:
cos θ=adjacent/hypotenuse

θ=35°
hypotenuse=h
adjacent=80 inches=6.66667 ft
thus;
cos 35=6.66667/h
h=6.66667/cos35
h=8.1385 ft
diagonal=8.1385 ft

we conclude that the table will through the door diagonally.