Divers looking for a sunken ship have defined the search area as a triangle with adjacent sides of lengths 2.75 and 1.32 the angle between the sides is 35 degrees. find the search area.
For a triangle where you know two sides and the contained angle Ø
the area is (1/2)(side1)(side2)sinØ
You have those 3 numbers, let me know what you get
Given: a = 2.75, b = 1.32, A = 35o.
Area = 0.5*a*b*sinA. = 0.5*2.75*1.32*sin35 = ___ sq. miles.
To find the search area of the triangle, we can use the formula for the area of a triangle: 1/2 * base * height.
In this case, the base of the triangle is the length of one of the adjacent sides, which is 2.75. The height is the perpendicular distance from the base to the opposite vertex, which we need to find.
To find the height, we can use trigonometry. Since we know the length of the adjacent side and the angle between the sides, we can use the trigonometric function tangent (tan).
Using the formula tan(angle) = opposite/adjacent, we can rearrange the formula to solve for the opposite side (height).
tan(35 degrees) = height/1.32
Now we can find the height:
height = tan(35 degrees) * 1.32
Using a calculator, we find that tan(35 degrees) is approximately 0.7002.
height ≈ 0.7002 * 1.32 ≈ 0.9248
Now we have the height (0.9248) and the base (2.75), we can calculate the search area:
Area = 1/2 * base * height
Area = 1/2 * 2.75 * 0.9248
Using a calculator, we find that the search area is approximately 1.272 square units.