QuestionGiven , , and , find if this forms 1, 2, or no triangles. Solve any triangles formed.
Studdy Solution
STEP 1
Assumptions1. Side a =8. Side b =3. Angle A =10 degrees4. We are dealing with a non-right triangle5. We are using the Law ofines to solve the triangle
STEP 2
The Law ofines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle. It can be written as
STEP 3
We can use the Law ofines to find angle B. Rearrange the formula to solve for B
STEP 4
Substitute the given values into the formula
STEP 5
Calculate the value of
STEP 6
Now, we need to find the angle B. Since the sine function can have two possible values (one in the first quadrant and one in the second quadrant), we need to find both possible values for B.The first possible value for B is
STEP 7
Calculate the first possible value for B
STEP 8
The second possible value for B is found by subtracting the first possible value from180 degrees
STEP 9
Calculate the second possible value for B
STEP 10
Now we need to check if these values for B are valid. In a triangle, the sum of all angles must be equal to180 degrees.For the first possible value of B, we calculate the third angle C
STEP 11
Substitute the values for A and B into the formula
STEP 12
Calculate the value for C
STEP 13
For the second possible value of B, we calculate the third angle C':
STEP 14
Substitute the values for A and B' into the formula
STEP 15
Calculate the value for C':
STEP 16
Since an angle in a triangle cannot be negative, the second possible value for B is not valid. Therefore, there is only one triangle that can be formed with the given values.
The triangle has the following sides and angles
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