Question

3. Divers looking for a sunken ship have defined the search area as a triangle with adjacent sides of length 2.75 miles and 1.32 miles. The angle between the sides of the triangle is 35. To the nearest hundredth, find the search area. 2.08 mi²

2.97 mi²
1.49 mi²
1.04 mi²

Answer 1

2.08 mi²

Explanation:

Since, the area of the triangle is,

`A=s_1* s_2* sin \theta`

Where,
`s_1` and
`s_2` are adjacent sides and
`\theta` is the included angle of these sides,

Here,
`s_1` = 2.75 miles,

`s_2` = 1.32 miles,

And,
`\theta` = 35°,

hence, the area of the given triangle is,

`A=2.75* 1.32* sin 35^(\circ)`

`= 3.63* 0.57357643635`

`= 2.08208246395\approx 2.08\text{ square miles}`

Answer 2

Area = (1/2) x 2.75 x 1.32 x sin(35 deg) = 1.815 x (0.573576) = 1.04 sq. miles.