Question

“I think I can make it. I’ll just jump.” says Denis, flashing a grin as he looks to the neighboring rooftop.

“Wait!” Vera exclaims. “First let's find the distance! Here, take a look at this diagram.”
“I’ve never much cared for math,” Denis frowns.
Vera rolls her eyes. “We know the distance between us, and we know the angles between ourselves and your target landing point. All we need to do is...”
Denis jumps.
“...apply the law of sines.” Vera gasps.
According to Vera's diagram, how far did Denis need to jump to reach the neighboring rooftop?

Answer 1

9514 1404 393

Answer:

5.3 m

Explanation:

The angle opposite the given side is ...

180° -105° -40° = 35°

Then the law of sines tells us the unknown distance (d) is ...

d/sin(40°) = 4.7 m/sin(35°)

d = (4.7 m)sin(40°)/sin(35°) ≈ 5.267 m

Denis will need to jump about 5.3 m to reach the neighboring roof.

_____

Additional comment

Denis will need a running start. The world record for a standing broad jump is less than 4 m.