Problem 37
Question
Find the area of the triangle having the indicated angle and sides. \(A=150^{\circ}, \quad b=8, \quad c=10\)
Step-by-Step Solution
Verified Answer
The area of the triangle is 20 square units.
1Step 1: Understand the formula
The formula used to calculate the area of a triangle when two sides and the included angle are given is: \(Area = 0.5 * Side1 * Side2 * sin(Angle)\)
2Step 2: Plugging in the given values
Here Side1 is given as 8, Side2 is given as 10 and Angle is given as 150 degrees. The formula becomes \(Area = 0.5 * 8 * 10 * sin(150)\)
3Step 3: Calculating the area
Now use a calculator to find the value of sin(150) approximately equals to 0.5. Substitute this value into the formula to get the area of the triangle, which is \( Area = 0.5*8*10*0.5 = 20\)
Other exercises in this chapter
Problem 37
Find (a) \(\mathbf{u}+\mathbf{v}\) (b) \(\mathbf{u}-\mathbf{v},(\mathbf{c})\) 2 \(\mathbf{u}-3 \mathbf{v},\) and (d) \(\frac{1}{2} \mathbf{v}+4 \mathbf{u} .\) T
View solution Problem 37
Determine whether the Law of sines or the Law of cosines can be used to find another measure of the triangle. Then solve the triangle. $$A=42^{\circ}, \quad B=3
View solution Problem 38
Use vectors to find the interior angles of the triangle with the given vertices. $$(-3,5), (-1,9), (7,9)$$
View solution Problem 38
Find (a) \(\mathbf{u}+\mathbf{v}\) (b) \(\mathbf{u}-\mathbf{v},(\mathbf{c})\) 2 \(\mathbf{u}-3 \mathbf{v},\) and (d) \(\frac{1}{2} \mathbf{v}+4 \mathbf{u} .\) T
View solution