The coordinates of the vertices of △GHI are G(−7,2), H(−2,2), and I(−2,8). Find the side lengths to the nearest hundredth and the angle measures to the nearest degree.

a) Side lengths

= GH = 5 units

HI = 6 units

GI = 7.81 units

b) Angle measures

Angle G = 39.81°

Angle H = 90°

Angle I = 50.2°

Step-by-step explanation:

The coordinates of the vertices of △GHI are G(−7,2), H(−2,2), and I(−2,8). Find the side lengths to the nearest hundredth and the angle measures to the nearest degree.

Step 1

We find the side lengths using the coordinates formula

= √(x2 - x1)² + (y2 - y1)²

When we are given vertices (x1, y1) and (x2 , y2)

Coordinates of the vertices of △GHI are G(−7,2), H(−2,2), and I(−2,8).

For side length

GH = G(−7,2), H(−2,2)

= √(-2 - (-7))² + (2 - 2)²

= √(-2 + 7)² + (0)²

= √5²

= √25

= 5 units

For side length HI

HI = H(−2,2), and I(−2,8)

= √(-2 -(-2))² + (8 - 2)²

= √(0)² + (6)²

= √36

= 6 units

For side length GI

G(−7,2), I(−2,8)

= √(-2 -(-7))² + (8 - 2)²

= √(5)² + (6)²

= √25 + 36

= √61

= 7.81 units

Step 2

Angle measures

We find this using Cosine rules

Angle a = arc cos (b² + c² - a²/2bc)

Hence:

Finding

Angle G = arc cos (6² + 7.81² - 5² / 2 × 6 × 7.81)

= 39.81°

Angle H = arc cos (5² + 6² - 7.81² / 2 × 5 × 6)

= 90°

Angle I = arc cos (5² + 7.81² - 5² / 2 × 5 × 7.81)

= 50.2°