Question

Find the area of the triangle. A. 27.8km^2 B. 32.8 km^2 C.14.9 km^2 D. 54.8km^2

Answer 1

Answer:

32.8 mi²

Step-by-step explanation:

Hi there!

Area of a triangle when given two sides, a and b, and the angle that conjoins them, C:

$A=\frac{1}{2} ab*sinC$

Plug in the known information:

a=11, b=6, C=97°

$A=\frac{1}{2} (11)(6)*sin(97)\\A=33sin(97)\\A=32.8$

Therefore, the area of the triangle is approximately 32.8 mi².

I hope this helps!

Answer 2

Answer:

B

Step-by-step explanation:

The trick here is to find the height. The answer is

height = sin(180 - 97) * 11

The height is found by finding the supplement of 97, taking the sin of that angle and multiplying by 11.

There is a drawing required. You need to extend ZY until a line from x meets ZY (extended) at right angles. When that happens you find the sine of the supplement.

height = sin(83)*11

height = 10.92

Now use the standard area formula.

Area = base (ZY) * height / 2

base = 6

height = 10.92

Area = 6 * 10.92 /2

Area = 32.75