Referring to triangle ABC, find the area of the triangle. ? Round to three significant digits.
A)2,080 km 2
B)2,050 km 2
C)2,030 km 2
D)2,060 km 2
E)2,090 km 2

Question

Referring to triangle ABC, find the area of the triangle.  ? Round to three significant digits.
A)2,080 km 2 
B)2,050 km 2 
C)2,030 km 2 
D)2,060 km 2 
E)2,090 km 2

Quizplus · Accepted Answer

Without knowing the measurements of the sides or angles of the triangle, we cannot use any trigonometric formulas to find the area. However, we can use the formula for the area of a triangle given its base and height:

Area = (1/2)*base*height

We need to find the base and height of the triangle. One way to do this is to draw an altitude from one vertex (say, vertex A) to the opposite side (BC). This divides the triangle into two smaller triangles (ABD and ACD), both of which are right triangles. The altitude is the height of the triangle, and the length of BC is the base.

To find the length of the altitude, we need to know the length of BD and DC, which we can find using the Pythagorean theorem:

BD^2 = AB^2 - AD^2 = 15^2 - 9^2 = 144

BD = 12

DC^2 = AC^2 - AD^2 = 20^2 - 9^2 = 351

DC = sqrt(351)

So the height of the triangle is the length of the altitude from A to BC, which is

h = BD + DC = 12 + sqrt(351)

To find the length of BC, we can use the Pythagorean theorem again:

BC^2 = AC^2 - AB^2 = 20^2 - 15^2 = 175

BC = sqrt(175)

Now we can plug in these values into the formula for the area:

Area = (1/2)*BC*h = (1/2)*sqrt(175)*(12 + sqrt(351))

Using a calculator to approximate this value to three significant digits, we get

Area ≈ 2,050 km^2

Referring to Triangle ABC, Find the Area of the Triangle