Question

Please help me with Geometry!

Answer 1

1.7 hrs

Explanation:

We can use cosine law to find the distance d:

`{d}^(2) = {a}^(2) + {b}^(2) - 2ab \cos( \gamma )`

where. a = 3 mi

b = 4 mi

gamma = 71.7°

d^2 = (3mi)^2 + (4 mi)^2 - 2(3 mi)(4 mi)cos(71.7)

= 9 mi^2 + 16 mi^2 -24cos(71.7)

= 17.464 mi^2

or

d = 4.2 mi

To find the time it takes for him to go from the cave to the waterfall, divide this distance d by his walking rate of 2.5 mi/hr:

t = d/v = 4.2 mi/2.5 mph

= 1.7 hrs