Question

TUTORS PLEASE HELP PLEASEEE

Answer 1

a = 4.5

b = 2.1

B = 25°

Solving for a, step-by-step explanation:

From angle A, we are given the hypotenuse (c = 5), the opposite side (solving for a), and angle A (A = 65°). We can use a trigonometric function to solve. Here, we will use sine.

`\displaystyle sin\theta=\frac{\text{opposite side}}{\text{hypotenuse}}`

`\displaystyle sin(65)=\frac{\text{a}}{\text{5}}`

5sin(65) = a

a = 4.5315 ≈ 4.5

Solving for b, step-by-step explanation:

Similar to solving for a, we will use a trigonometric function to solve. Here, we will use cosine. We are given the hypotenuse (c = 5), adjacent side (solving for b), and angle A (A = 65°).

`\displaystyle cos\theta=\frac{\text{adjacent side}}{\text{hypotenuse}}`

`\displaystyle cos(65)=\frac{\text{b}}{\text{5}}`

5cos(65) = 5

a = 2.11309 ≈ 2.1

Solving for B, step-by-step explanation:

We know that a triangle's angles add up to 180 degrees. Since we are given that this is a right triangle (90°) and that A is equal to 65 degrees, we can solve for B with a pretty simple subtraction equation.

180° - 90° - 65° = B

25° = B

B = 25°