Find the area of the triangle with vertices: q(3,-4,-5), r(4,-1,-4), s(3,-5,-6).
1 answer:
Answer:
(√6)/2 square units
Step-by-step explanation:
The area of a triangle is half the magnitude of the cross product of the vectors representing adjacent sides.
QR = (4-3, -1-(-4), -4-(-5)) = (1, 3, 1)
QS = (3 -3, -5-(-4), -6-(-5)) = (0, -1, -1)
The cross product is the determinant ...
The magnitude of this is ...
|QR × QS| = √((-2)² +1² +(-1)²) = √6
The area of the triangle is half this value:
Area = (1/2)√6 . . . . square units
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This seems like a right triangle problem.
So assuming 14 feet is the hypotenuse and 4 feet is a leg of the right triangle, we can use the pythagorean theorem () to solve for the height of the house, in which we shall name it x.
So, the equation is .
Solve for x:
16+x^{2}= 196
x^{2}= 196-16
x^{2}= 180
x = 6√5 feet
Hope this helps!