Question

Please help I will give brainliest

Answer 1

Answer:

1. ∠YZX = 37°

2. ∠YXZ = 53°

3. XZ = 30 meters

Step-by-step explanation:

1. To solve for an unknown angle, we need to utilize the inverse of a trigonometric function.

⭐What are the inverses of the trigonometric functions?

• $sin^-1 (opposite/hypotenuse)$
• $cos^-1 (adjacent/hypotenuse)$
• $tan^-1(opposite/adjacent)$

To know which inverse of the trigonometric functions we use, we have to see the type of side lengths we are given (opposite, adjacent, or hypotenuse)

We are given side length XY, which is opposite of ∠YZX, and we are given side length YZ, which is adjacent to ∠YZX. Therefore, we will use $tan^-1 (opposite/adjacent) =$

Substitute the values we are given into the function:

$tan^-1 (18/24) =$

Compute this equation using a scientific calculator. I recommend using the Desmos Scientific Calculator:

$= 37$

∴ ∠YZX = 37°

2. We already know 2 angles (∠YZX = 37°, and ∠ZYX = 90°) Therefore, to find ∠YXZ, we have to utilize the triangle sum theorem.

⭐ What is the triangle sum theorem?

• $angle_1 + angle_2 +angle_3 = 180$
• The sum of all angles in a triangle is 180°

Substitute the angles we know already (∠YZX and ∠ZYX), and solve for ∠YXZ.

$< YZX + < ZYX + < YXZ = 180$

$37 + 90 + YXZ = 180$

$127 + YXZ = 180$

$< YXZ = 53$

∴ ∠YXZ = 53°

3. We already know 2 side lengths (ZY = 24 meters, and XY = 18). Therefore, to find XZ, we have to utilize the Pythagoras' theorem.

⭐ What is the Pythagoras' theorem?

• $(C)^2 = (A)^2 + (B)^2$
• C is the hypotenuse of the triangle, A is a leg of the triangle, and B is another leg of the triangle
• Pythagoras' theorem can only be used on right triangles

Substitute the values of the side lengths into the formula:

$(XZ)^2 = (XY)^2 + (ZY)^2$

$(XZ)^2 = 18^2 + 24^2$

Solve for XZ:

$(XZ)^2 = 324 + 576$

$(XZ)^2 = 900$

$\sqrt{(XZ)^2} = \sqrt{900}$

$XZ = 30$

∴ XZ = 30 meters