Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution.Find the area of the shaded region bounded by the triangle with vertices (0,0), (7,8), (15,0).
A)precalculus , 60.0
B)precalculus , 120.0
C)calculus , 180.0
D)calculus , 120.0
E)precalculus , 180.0

Question

Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution.Find the area of the shaded region bounded by the triangle with vertices (0,0), (7,8), (15,0). 
A)precalculus , 60.0 
B)precalculus , 120.0 
C)calculus , 180.0 
D)calculus , 120.0 
E)precalculus , 180.0

Quizplus · Accepted Answer

The shaded region is a triangle, and we can find its area using the formula for the area of a triangle:

A = 1/2 * base * height

The base of the triangle is 15 - 0 = 15, and the height is the distance from the line segment connecting (0,0) and (15,0) to the point (7,8). To find this distance, we can use the formula for the distance between a point and a line:

d = |Ax + By + C| / sqrt(A^2 + B^2)

where (x,y) is the point and the line is given in the form Ax + By + C = 0.

The line segment connecting (0,0) and (15,0) can be represented by the equation y = 0. Plugging in the coordinates of the point (7,8), we get:

d = |0*7 + (-1)*8 + 0| / sqrt(0^2 + (-1)^2) = 8

Therefore, the height of the triangle is 8, and its area is:

A = 1/2 * base * height = 1/2 * 15 * 8 = 60.

So the answer is choice A, precalculus, 60.0.

Decide Whether the Following Problem Can Be Solved Using Precalculus