Answer:
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°
