Question

Solve the following triangle for all missing sides and angles.
Part I: What is the measure of angle A?
Part II: Use the law of sines to find the length of side a.
Part III: Use the law of cosines to find the length of side b.
Can someone please help?I'll give extra points and mark as brainliest.
PLEASEEEEEE!!!

Answer 1

Answer:

Part 1: 100

Part 2: 29.19 (Rounded)

Part 3: 20.96 (Rounded)

Step-by-step explanation:

Part 1: Triangle Sum Theorem (All angles of a triangle add up to 180 degrees)

45 + 35 + A = 180

80 + A = 180

Move the constant to the other side

80 + A = 180

-80          -80

A = 80°

Part 2: Law of sines

$\frac{a}{sin(100)} = \frac{17}{sin(35)}$

Cross multiplication

sin(35)a = 16.7417318

Divide both sides by sin(35)

a = 29.18831866

Part 3: Law of cosines

$b=29.19^{2}+17^{2}-2*29.19*17*cos(45)$ = 439.2809039

Square root the answer

$\sqrt{439.2809039}$ =20.95902917

Answer 2

The value of angle A is 100 degrees and the measure of side a is 29.2 and b is 20.96.

What is a Triangle?

A triangle is a polygon with three sides, angles, and vertices.

The triangle ABC, has AB = 17, angle ABC = 45 degree, angle ACB = 35 degree.

The measure of angle A can be determined by using the angle sum property.

45 + 35 + A = 180

80 + A = 180

A = 180-80

A = 100 degree.

Using the law of sines to find the length of side a,

a/ sin A = b/ sin B = c/sin C

a/ sin100 = 17/ sin 35

a = 17 * sin 100 / sin35

a = 29.2

Use the law of cosines to find the length of side b.

b² = c² +a² -2ac cos B

b² = (17)² + (29.2)² - 2* 17* 29.2 cos 45

b² = 439.23

b = 20.96

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