Find, correct to the nearest degree, the three angles of the triangle with the given vertices. a(1, 0, −1), b(5, −4, 0), c(1, 4, 5)

The three angles are 43.11°, 103.95° and 32.94°.

Step-by-step explanation:

Let us name the corresponding angles to A, B and C to be ∠a, ∠b and ∠c respectively as shown in the figure below.

Using the vector representation of lines, we get,

Vector AB = < 1-5, 0+4, -1-0 > = < -4, 4, -1 >

Vector AC = < 1-5, 4+4, 5-0 > = < -4, 8, 5 >

Also, we have the modulus value given by,

|AB| = = = 5.75

|AC| = = = 10.25

Now, using the dot product, we have,

AB · AC = |AB| |AC| cos(a)

i.e.

i.e.

i.e.

i.e.

i.e.

Hence, ∠a = 43.11°

Again, we see that,

Vector BA = < 5-1, -4-0, 0+1 > = < 4, -4, 1 >

Vector BC = < 1-1,4-0, 5+1 > = < 0, 4, 6 >

Also, we have the modulus value given by,

|Ba| = = = 5.75

|BC| = = = 7.21

Now, using the dot product, we have,

BA · BC = |BA| |BC| cos(b)

i.e.

i.e.

i.e.

i.e.

i.e.

Hence, ∠b = 103.95°

Since, the sum of all the angles in a triangle is 180°.

Thus, ∠a + ∠b + ∠c = 180°

i.e. 43.11° + 103.95° + ∠c = 180°

i.e. ∠c = 180° - 147.06°

i.e. ∠c = 32.94°

Hence, the three angles are 43.11°, 103.95° and 32.94°.

answer: the answer is 30 miles per hour.

ft/s -> mphmph = ft/s 1.466667mph = 44 divided by 1.466667mph = 30.00000

- r3ktforgood ☕

step-by-step explanation:

if you want to solve percent error follow these steps.

1. subtract the accepted value from the experimental value.

2. take the absolute value of step 1.

3. divide that answer by the accepted value.

4. multiply that answer by 100 and add the % symbol to express the answer as a percentage.

if you want to solve percent of change just do this.

1. work out the difference (increase) between the two numbers you are comparing.

2. divide the increase by the original number and multiply the answer by 100. if your answer is a negative number then this is a percentage decrease.

hope this : )