in triangle ABC, angle a=120, b=10, and c=18. What is the area of triangle ABC tot he nearest square inch?
perfect setup for using
area = (1/2)(b)(c)sin A, where A is the contained angle.
area = (1/2)(10)(18)sin 120°
= 77.94 or 45√3 as an exact value.
To find the area of triangle ABC, we can use the trigonometric formula:
Area = (1/2) * a * b * sin(C)
Given that angle A = 120°, angle B = 10°, and angle C = 18°, we can substitute the values into the formula.
Area = (1/2) * 120 * 10 * sin(18)
To calculate sin(18), we need to use a scientific calculator or mathematical software.
sin(18) is approximately 0.309
Substituting this value into the equation:
Area = (1/2) * 120 * 10 * 0.309
Area = 185.4 square units
Therefore, the area of triangle ABC is approximately 185.4 square inches.
To find the area of triangle ABC, we can use the formula for the area of a triangle:
Area = (1/2) * base * height
In this case, we don't have the base and height directly given. Instead, we are given the measures of the angles of triangle ABC. To find the missing side lengths, we need to use the Law of Sines or the Law of Cosines.
Let's use the Law of Sines to find the missing side lengths. The Law of Sines states that in any triangle:
a/sin(A) = b/sin(B) = c/sin(C)
Given that angle A has a measure of 120 degrees and side a is opposite to angle A, we have:
a/sin(120) = b/sin(B) = c/sin(C)
Now we can calculate the missing side lengths:
a/sin(120) = b/sin(B)
a/sin(120) = 10/sin(B)
Using the Law of Sines, we can solve for side a:
a = (10 * sin(120)) / sin(B)
Similarly, we can find side c:
c = (18 * sin(120)) / sin(C)
Now that we have the side lengths of the triangle, we can use the formula for the area of a triangle. Let's assume side a is the base of the triangle, and the height is the perpendicular dropped from the opposite vertex (angle C) to side a.
To find the height, we can use the sine formula:
height = c * sin(B)
Now we have all the required values to calculate the area of the triangle:
Area = (1/2) * base * height
Area = (1/2) * a * height
Evaluate these expressions to find the approximate area of triangle ABC to the nearest square inch.